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About this unit.
Significance tests give us a formal process for using sample data to evaluate the likelihood of some claim about a population value. Learn how to conduct significance tests and calculate p-values to see how likely a sample result is to occur by random chance. You'll also see how we use p-values to make conclusions about hypotheses.
Hypothesis Definition, Format, Examples, and Tips
Kendra Cherry, MS, is a psychosocial rehabilitation specialist, psychology educator, and author of the "Everything Psychology Book."
Amy Morin, LCSW, is a psychotherapist and international bestselling author. Her books, including "13 Things Mentally Strong People Don't Do," have been translated into more than 40 languages. Her TEDx talk, "The Secret of Becoming Mentally Strong," is one of the most viewed talks of all time.
Verywell / Alex Dos Diaz
Falsifiability of a hypothesis.
Hypotheses examples.
A hypothesis is a tentative statement about the relationship between two or more variables. It is a specific, testable prediction about what you expect to happen in a study. It is a preliminary answer to your question that helps guide the research process.
Consider a study designed to examine the relationship between sleep deprivation and test performance. The hypothesis might be: "This study is designed to assess the hypothesis that sleep-deprived people will perform worse on a test than individuals who are not sleep-deprived."
A hypothesis is crucial to scientific research because it offers a clear direction for what the researchers are looking to find. This allows them to design experiments to test their predictions and add to our scientific knowledge about the world. This article explores how a hypothesis is used in psychology research, how to write a good hypothesis, and the different types of hypotheses you might use.
In the scientific method , whether it involves research in psychology, biology, or some other area, a hypothesis represents what the researchers think will happen in an experiment. The scientific method involves the following steps:
The hypothesis is a prediction, but it involves more than a guess. Most of the time, the hypothesis begins with a question which is then explored through background research. At this point, researchers then begin to develop a testable hypothesis.
Unless you are creating an exploratory study, your hypothesis should always explain what you expect to happen.
In a study exploring the effects of a particular drug, the hypothesis might be that researchers expect the drug to have some type of effect on the symptoms of a specific illness. In psychology, the hypothesis might focus on how a certain aspect of the environment might influence a particular behavior.
Remember, a hypothesis does not have to be correct. While the hypothesis predicts what the researchers expect to see, the goal of the research is to determine whether this guess is right or wrong. When conducting an experiment, researchers might explore numerous factors to determine which ones might contribute to the ultimate outcome.
In many cases, researchers may find that the results of an experiment do not support the original hypothesis. When writing up these results, the researchers might suggest other options that should be explored in future studies.
In many cases, researchers might draw a hypothesis from a specific theory or build on previous research. For example, prior research has shown that stress can impact the immune system. So a researcher might hypothesize: "People with high-stress levels will be more likely to contract a common cold after being exposed to the virus than people who have low-stress levels."
In other instances, researchers might look at commonly held beliefs or folk wisdom. "Birds of a feather flock together" is one example of folk adage that a psychologist might try to investigate. The researcher might pose a specific hypothesis that "People tend to select romantic partners who are similar to them in interests and educational level."
So how do you write a good hypothesis? When trying to come up with a hypothesis for your research or experiments, ask yourself the following questions:
Before you come up with a specific hypothesis, spend some time doing background research. Once you have completed a literature review, start thinking about potential questions you still have. Pay attention to the discussion section in the journal articles you read . Many authors will suggest questions that still need to be explored.
To form a hypothesis, you should take these steps:
In the scientific method , falsifiability is an important part of any valid hypothesis. In order to test a claim scientifically, it must be possible that the claim could be proven false.
Students sometimes confuse the idea of falsifiability with the idea that it means that something is false, which is not the case. What falsifiability means is that if something was false, then it is possible to demonstrate that it is false.
One of the hallmarks of pseudoscience is that it makes claims that cannot be refuted or proven false.
A variable is a factor or element that can be changed and manipulated in ways that are observable and measurable. However, the researcher must also define how the variable will be manipulated and measured in the study.
Operational definitions are specific definitions for all relevant factors in a study. This process helps make vague or ambiguous concepts detailed and measurable.
For example, a researcher might operationally define the variable " test anxiety " as the results of a self-report measure of anxiety experienced during an exam. A "study habits" variable might be defined by the amount of studying that actually occurs as measured by time.
These precise descriptions are important because many things can be measured in various ways. Clearly defining these variables and how they are measured helps ensure that other researchers can replicate your results.
One of the basic principles of any type of scientific research is that the results must be replicable.
Replication means repeating an experiment in the same way to produce the same results. By clearly detailing the specifics of how the variables were measured and manipulated, other researchers can better understand the results and repeat the study if needed.
Some variables are more difficult than others to define. For example, how would you operationally define a variable such as aggression ? For obvious ethical reasons, researchers cannot create a situation in which a person behaves aggressively toward others.
To measure this variable, the researcher must devise a measurement that assesses aggressive behavior without harming others. The researcher might utilize a simulated task to measure aggressiveness in this situation.
The hypothesis you use will depend on what you are investigating and hoping to find. Some of the main types of hypotheses that you might use include:
A hypothesis often follows a basic format of "If {this happens} then {this will happen}." One way to structure your hypothesis is to describe what will happen to the dependent variable if you change the independent variable .
The basic format might be: "If {these changes are made to a certain independent variable}, then we will observe {a change in a specific dependent variable}."
Once a researcher has formed a testable hypothesis, the next step is to select a research design and start collecting data. The research method depends largely on exactly what they are studying. There are two basic types of research methods: descriptive research and experimental research.
Descriptive research such as case studies , naturalistic observations , and surveys are often used when conducting an experiment is difficult or impossible. These methods are best used to describe different aspects of a behavior or psychological phenomenon.
Once a researcher has collected data using descriptive methods, a correlational study can examine how the variables are related. This research method might be used to investigate a hypothesis that is difficult to test experimentally.
Experimental methods are used to demonstrate causal relationships between variables. In an experiment, the researcher systematically manipulates a variable of interest (known as the independent variable) and measures the effect on another variable (known as the dependent variable).
Unlike correlational studies, which can only be used to determine if there is a relationship between two variables, experimental methods can be used to determine the actual nature of the relationship—whether changes in one variable actually cause another to change.
The hypothesis is a critical part of any scientific exploration. It represents what researchers expect to find in a study or experiment. In situations where the hypothesis is unsupported by the research, the research still has value. Such research helps us better understand how different aspects of the natural world relate to one another. It also helps us develop new hypotheses that can then be tested in the future.
Thompson WH, Skau S. On the scope of scientific hypotheses . R Soc Open Sci . 2023;10(8):230607. doi:10.1098/rsos.230607
Taran S, Adhikari NKJ, Fan E. Falsifiability in medicine: what clinicians can learn from Karl Popper [published correction appears in Intensive Care Med. 2021 Jun 17;:]. Intensive Care Med . 2021;47(9):1054-1056. doi:10.1007/s00134-021-06432-z
Eyler AA. Research Methods for Public Health . 1st ed. Springer Publishing Company; 2020. doi:10.1891/9780826182067.0004
Nosek BA, Errington TM. What is replication ? PLoS Biol . 2020;18(3):e3000691. doi:10.1371/journal.pbio.3000691
Aggarwal R, Ranganathan P. Study designs: Part 2 - Descriptive studies . Perspect Clin Res . 2019;10(1):34-36. doi:10.4103/picr.PICR_154_18
Nevid J. Psychology: Concepts and Applications. Wadworth, 2013.
By Kendra Cherry, MSEd Kendra Cherry, MS, is a psychosocial rehabilitation specialist, psychology educator, and author of the "Everything Psychology Book."
Content preview.
Arcu felis bibendum ut tristique et egestas quis:
10.1 - setting the hypotheses: examples.
A significance test examines whether the null hypothesis provides a plausible explanation of the data. The null hypothesis itself does not involve the data. It is a statement about a parameter (a numerical characteristic of the population). These population values might be proportions or means or differences between means or proportions or correlations or odds ratios or any other numerical summary of the population. The alternative hypothesis is typically the research hypothesis of interest. Here are some examples.
About 10% of the human population is left-handed. Suppose a researcher at Penn State speculates that students in the College of Arts and Architecture are more likely to be left-handed than people found in the general population. We only have one sample since we will be comparing a population proportion based on a sample value to a known population value.
A generic brand of the anti-histamine Diphenhydramine markets a capsule with a 50 milligram dose. The manufacturer is worried that the machine that fills the capsules has come out of calibration and is no longer creating capsules with the appropriate dosage.
Many people are starting to prefer vegetarian meals on a regular basis. Specifically, a researcher believes that females are more likely than males to eat vegetarian meals on a regular basis.
Obesity is a major health problem today. Research is starting to show that people may be able to lose more weight on a low carbohydrate diet than on a low fat diet.
This research question might also be addressed like example 11.4 by making the hypotheses about comparing the proportion of stroke patients that live with smokers to the proportion of controls that live with smokers.
Step 1: define the hypothesis, step 2: set the criteria, step 3: calculate the statistic, step 4: reach a conclusion, types of errors, the bottom line.
Charlene Rhinehart is a CPA , CFE, chair of an Illinois CPA Society committee, and has a degree in accounting and finance from DePaul University.
Your investment advisor proposes you a monthly income investment plan that promises a variable return each month. You will invest in it only if you are assured of an average $180 monthly income. Your advisor also tells you that for the past 300 months, the scheme had investment returns with an average value of $190 and a standard deviation of $75. Should you invest in this scheme? Hypothesis testing comes to the aid for such decision-making.
Hypothesis or significance testing is a mathematical model for testing a claim, idea or hypothesis about a parameter of interest in a given population set, using data measured in a sample set. Calculations are performed on selected samples to gather more decisive information about the characteristics of the entire population, which enables a systematic way to test claims or ideas about the entire dataset.
Here is a simple example: A school principal reports that students in their school score an average of 7 out of 10 in exams. To test this “hypothesis,” we record marks of say 30 students (sample) from the entire student population of the school (say 300) and calculate the mean of that sample. We can then compare the (calculated) sample mean to the (reported) population mean and attempt to confirm the hypothesis.
To take another example, the annual return of a particular mutual fund is 8%. Assume that mutual fund has been in existence for 20 years. We take a random sample of annual returns of the mutual fund for, say, five years (sample) and calculate its mean. We then compare the (calculated) sample mean to the (claimed) population mean to verify the hypothesis.
This article assumes readers' familiarity with concepts of a normal distribution table, formula, p-value and related basics of statistics.
Different methodologies exist for hypothesis testing, but the same four basic steps are involved:
Usually, the reported value (or the claim statistics) is stated as the hypothesis and presumed to be true. For the above examples, the hypothesis will be:
This stated description constitutes the “ Null Hypothesis (H 0 ) ” and is assumed to be true – the way a defendant in a jury trial is presumed innocent until proven guilty by the evidence presented in court. Similarly, hypothesis testing starts by stating and assuming a “ null hypothesis ,” and then the process determines whether the assumption is likely to be true or false.
The important point to note is that we are testing the null hypothesis because there is an element of doubt about its validity. Whatever information that is against the stated null hypothesis is captured in the Alternative Hypothesis (H 1 ). For the above examples, the alternative hypothesis will be:
In other words, the alternative hypothesis is a direct contradiction of the null hypothesis.
As in a trial, the jury assumes the defendant's innocence (null hypothesis). The prosecutor has to prove otherwise (alternative hypothesis). Similarly, the researcher has to prove that the null hypothesis is either true or false. If the prosecutor fails to prove the alternative hypothesis, the jury has to let the defendant go (basing the decision on the null hypothesis). Similarly, if the researcher fails to prove an alternative hypothesis (or simply does nothing), then the null hypothesis is assumed to be true.
The decision-making criteria have to be based on certain parameters of datasets.
The decision-making criteria have to be based on certain parameters of datasets and this is where the connection to normal distribution comes into the picture.
As per the standard statistics postulate about sampling distribution , for any sample size n, the sampling distribution of X is normal if the X from which the sample is drawn is normally distributed. Hence, the probabilities of all other possible sample mean that one could select are normally distributed.
For e.g., determine if the average daily return, of any stock listed on XYZ stock market , around New Year's Day is greater than 2%.
H 0 : Null Hypothesis: mean = 2%
H 1 : Alternative Hypothesis: mean > 2% (this is what we want to prove)
Take the sample (say of 50 stocks out of total 500) and compute the mean of the sample.
For a normal distribution, 95% of the values lie within two standard deviations of the population mean. Hence, this normal distribution and central limit assumption for the sample dataset allows us to establish 5% as a significance level. It makes sense as, under this assumption, there is less than a 5% probability (100-95) of getting outliers that are beyond two standard deviations from the population mean. Depending upon the nature of datasets, other significance levels can be taken at 1%, 5% or 10%. For financial calculations (including behavioral finance), 5% is the generally accepted limit. If we find any calculations that go beyond the usual two standard deviations, then we have a strong case of outliers to reject the null hypothesis.
Graphically, it is represented as follows:
In the above example, if the mean of the sample is much larger than 2% (say 3.5%), then we reject the null hypothesis. The alternative hypothesis (mean >2%) is accepted, which confirms that the average daily return of the stocks is indeed above 2%.
However, if the mean of the sample is not likely to be significantly greater than 2% (and remains at, say, around 2.2%), then we CANNOT reject the null hypothesis. The challenge comes on how to decide on such close range cases. To make a conclusion from selected samples and results, a level of significance is to be determined, which enables a conclusion to be made about the null hypothesis. The alternative hypothesis enables establishing the level of significance or the "critical value” concept for deciding on such close range cases.
According to the textbook standard definition, “A critical value is a cutoff value that defines the boundaries beyond which less than 5% of sample means can be obtained if the null hypothesis is true. Sample means obtained beyond a critical value will result in a decision to reject the null hypothesis." In the above example, if we have defined the critical value as 2.1%, and the calculated mean comes to 2.2%, then we reject the null hypothesis. A critical value establishes a clear demarcation about acceptance or rejection.
This step involves calculating the required figure(s), known as test statistics (like mean, z-score , p-value , etc.), for the selected sample. (We'll get to these in a later section.)
With the computed value(s), decide on the null hypothesis. If the probability of getting a sample mean is less than 5%, then the conclusion is to reject the null hypothesis. Otherwise, accept and retain the null hypothesis.
There can be four possible outcomes in sample-based decision-making, with regard to the correct applicability to the entire population:
|
| |
| Correct | Incorrect (TYPE 1 Error - a) |
| Incorrect (TYPE 2 Error - b) | Correct |
The “Correct” cases are the ones where the decisions taken on the samples are truly applicable to the entire population. The cases of errors arise when one decides to retain (or reject) the null hypothesis based on the sample calculations, but that decision does not really apply for the entire population. These cases constitute Type 1 ( alpha ) and Type 2 ( beta ) errors, as indicated in the table above.
Selecting the correct critical value allows eliminating the type-1 alpha errors or limiting them to an acceptable range.
Alpha denotes the error on the level of significance and is determined by the researcher. To maintain the standard 5% significance or confidence level for probability calculations, this is retained at 5%.
According to the applicable decision-making benchmarks and definitions:
A few more examples will demonstrate this and other calculations.
A monthly income investment scheme exists that promises variable monthly returns. An investor will invest in it only if they are assured of an average $180 monthly income. The investor has a sample of 300 months’ returns which has a mean of $190 and a standard deviation of $75. Should they invest in this scheme?
Let’s set up the problem. The investor will invest in the scheme if they are assured of the investor's desired $180 average return.
H 0 : Null Hypothesis: mean = 180
H 1 : Alternative Hypothesis: mean > 180
Identify a critical value X L for the sample mean, which is large enough to reject the null hypothesis – i.e. reject the null hypothesis if the sample mean >= critical value X L
P (identify a Type I alpha error) = P (reject H 0 given that H 0 is true),
This would be achieved when the sample mean exceeds the critical limits.
= P (given that H 0 is true) = alpha
Graphically, it appears as follows:
Taking alpha = 0.05 (i.e. 5% significance level), Z 0.05 = 1.645 (from the Z-table or normal distribution table)
= > X L = 180 +1.645*(75/sqrt(300)) = 187.12
Since the sample mean (190) is greater than the critical value (187.12), the null hypothesis is rejected, and the conclusion is that the average monthly return is indeed greater than $180, so the investor can consider investing in this scheme.
One can also use standardized value z.
Test Statistic, Z = (sample mean – population mean) / (std-dev / sqrt (no. of samples).
Then, the rejection region becomes the following:
Z= (190 – 180) / (75 / sqrt (300)) = 2.309
Our rejection region at 5% significance level is Z> Z 0.05 = 1.645.
Since Z= 2.309 is greater than 1.645, the null hypothesis can be rejected with a similar conclusion mentioned above.
We aim to identify P (sample mean >= 190, when mean = 180).
= P (Z >= (190- 180) / (75 / sqrt (300))
= P (Z >= 2.309) = 0.0084 = 0.84%
The following table to infer p-value calculations concludes that there is confirmed evidence of average monthly returns being higher than 180:
p-value | Inference |
less than 1% | supporting alternative hypothesis |
between 1% and 5% | supporting alternative hypothesis |
between 5% and 10% | supporting alternative hypothesis |
greater than 10% | supporting alternative hypothesis |
A new stockbroker (XYZ) claims that their brokerage fees are lower than that of your current stock broker's (ABC). Data available from an independent research firm indicates that the mean and std-dev of all ABC broker clients are $18 and $6, respectively.
A sample of 100 clients of ABC is taken and brokerage charges are calculated with the new rates of XYZ broker. If the mean of the sample is $18.75 and std-dev is the same ($6), can any inference be made about the difference in the average brokerage bill between ABC and XYZ broker?
H 0 : Null Hypothesis: mean = 18
H 1 : Alternative Hypothesis: mean <> 18 (This is what we want to prove.)
Rejection region: Z <= - Z 2.5 and Z>=Z 2.5 (assuming 5% significance level, split 2.5 each on either side).
Z = (sample mean – mean) / (std-dev / sqrt (no. of samples))
= (18.75 – 18) / (6/(sqrt(100)) = 1.25
This calculated Z value falls between the two limits defined by:
- Z 2.5 = -1.96 and Z 2.5 = 1.96.
This concludes that there is insufficient evidence to infer that there is any difference between the rates of your existing broker and the new broker.
Alternatively, The p-value = P(Z< -1.25)+P(Z >1.25)
= 2 * 0.1056 = 0.2112 = 21.12% which is greater than 0.05 or 5%, leading to the same conclusion.
Graphically, it is represented by the following:
Criticism Points for the Hypothetical Testing Method:
Hypothesis testing allows a mathematical model to validate a claim or idea with a certain confidence level. However, like the majority of statistical tools and models, it is bound by a few limitations. The use of this model for making financial decisions should be considered with a critical eye, keeping all dependencies in mind. Alternate methods like Bayesian Inference are also worth exploring for similar analysis.
Gregory J. Privitera. " Chapter 8: Introduction to Hypothesis Testing ." Statistics for Behavioral Sciences, Part III: Probability and the Foundations of Inferential Statistics. Sage Publications , pp. 4-5.
Rice University, OpenStax. " Introductory Statistics 2e: 7.1 The Central Limit Theorem for Sample Means (Averages) ."
Gregory J. Privitera. " Chapter 8: Introduction to Hypothesis Testing ." Statistics for Behavioral Sciences, Part III: Probability and the Foundations of Inferential Statistics. Sage Publications , pp. 5-6.
Gregory J. Privitera. " Chapter 8: Introduction to Hypothesis Testing ." Statistics for Behavioral Sciences, Part III: Probability and the Foundations of Inferential Statistics. Sage Publications , pp. 13.
Gregory J. Privitera. " Chapter 8: Introduction to Hypothesis Testing ." Statistics for Behavioral Sciences, Part III: Probability and the Foundations of Inferential Statistics. Sage Publications , pp. 6.
Gregory J. Privitera. " Chapter 8: Introduction to Hypothesis Testing ." Statistics for Behavioral Sciences, Part III: Probability and the Foundations of Inferential Statistics. Sage Publications , pp. 6-7.
Gregory J. Privitera. " Chapter 8: Introduction to Hypothesis Testing ." Statistics for Behavioral Sciences, Part III: Probability and the Foundations of Inferential Statistics. Sage Publications , pp. 10.
Gregory J. Privitera. " Chapter 8: Introduction to Hypothesis Testing ." Statistics for Behavioral Sciences, Part III: Probability and the Foundations of Inferential Statistics. Sage Publications , pp. 11.
Gregory J. Privitera. " Chapter 8: Introduction to Hypothesis Testing ." Statistics for Behavioral Sciences, Part III: Probability and the Foundations of Inferential Statistics. Sage Publications , pp. 7, 10-11.
Statistics Made Easy
In statistics, hypothesis tests are used to test whether or not some hypothesis about a population parameter is true.
To perform a hypothesis test in the real world, researchers will obtain a random sample from the population and perform a hypothesis test on the sample data, using a null and alternative hypothesis:
If the p-value of the hypothesis test is less than some significance level (e.g. α = .05), then we can reject the null hypothesis and conclude that we have sufficient evidence to say that the alternative hypothesis is true.
The following examples provide several situations where hypothesis tests are used in the real world.
Hypothesis tests are often used in biology to determine whether some new treatment, fertilizer, pesticide, chemical, etc. causes increased growth, stamina, immunity, etc. in plants or animals.
For example, suppose a biologist believes that a certain fertilizer will cause plants to grow more during a one-month period than they normally do, which is currently 20 inches. To test this, she applies the fertilizer to each of the plants in her laboratory for one month.
She then performs a hypothesis test using the following hypotheses:
If the p-value of the test is less than some significance level (e.g. α = .05), then she can reject the null hypothesis and conclude that the fertilizer leads to increased plant growth.
Hypothesis tests are often used in clinical trials to determine whether some new treatment, drug, procedure, etc. causes improved outcomes in patients.
For example, suppose a doctor believes that a new drug is able to reduce blood pressure in obese patients. To test this, he may measure the blood pressure of 40 patients before and after using the new drug for one month.
He then performs a hypothesis test using the following hypotheses:
If the p-value of the test is less than some significance level (e.g. α = .05), then he can reject the null hypothesis and conclude that the new drug leads to reduced blood pressure.
Hypothesis tests are often used in business to determine whether or not some new advertising campaign, marketing technique, etc. causes increased sales.
For example, suppose a company believes that spending more money on digital advertising leads to increased sales. To test this, the company may increase money spent on digital advertising during a two-month period and collect data to see if overall sales have increased.
They may perform a hypothesis test using the following hypotheses:
If the p-value of the test is less than some significance level (e.g. α = .05), then the company can reject the null hypothesis and conclude that increased digital advertising leads to increased sales.
Hypothesis tests are also used often in manufacturing plants to determine if some new process, technique, method, etc. causes a change in the number of defective products produced.
For example, suppose a certain manufacturing plant wants to test whether or not some new method changes the number of defective widgets produced per month, which is currently 250. To test this, they may measure the mean number of defective widgets produced before and after using the new method for one month.
They can then perform a hypothesis test using the following hypotheses:
If the p-value of the test is less than some significance level (e.g. α = .05), then the plant can reject the null hypothesis and conclude that the new method leads to a change in the number of defective widgets produced per month.
Introduction to Hypothesis Testing Introduction to the One Sample t-test Introduction to the Two Sample t-test Introduction to the Paired Samples t-test
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saubhagya verma
Analytics Vidhya
Have you ever wondered what is the total number of corn buds in corn? Probably not! This is because corns aren’t that important to us. They don’t form a major part of our expenses.
However, for Kellogg’s calculating the number of corn buds in corn is a big deal. The famous Corn Flakes of Kellogg’s are made by processing these corn buds. Since corn buds form a major part of their final product, it is important for them to know about the number of buds in corn so that they can predict the number of Corn Flakes.
Let us suppose that a corn bud contains around 70 buds on average and each corn is priced the same as 10 rupees. Also, the corn bud to cornflake ratio (input to output ratio) is 1:1 and the price of 70 units of cornflake is 40 rupees. So on average, the profit generated by the company will be approximately 30 rupees on each such corn assuming that the company has no other costs.
So here you can see how the number of buds in corn can impact the profitability of a multi-billion dollar company. We use Hypothesis testing to find the answers to these kinds of claims (a corn bud contains around 70 buds on average) by using statistics. This testing helps us to understand the likelihood that the claim will be true or not based upon a sample of inputs. Let us understand the basic concepts that are instrumental for doing hypothesis testing.
In layman's terms, the hypothesis is an assumption or a proposed explanation about a phenomenon. We formulate hypotheses whenever we aren’t sure about the real value of a population parameter. So, we assume a particular value for the population parameter to test a claim against it. Some examples of hypotheses are shown below:-
3. Point Estimate : A point estimate involves the calculation of a single best value that is representative of the unknown population parameter. We use a point estimate to find a value that acts as a central tendency for the population parameter. There are two methods commonly used to calculate point estimates:-
4. Confidence Interval : We use confidence intervals to find a range of estimate values that the population parameters can take based upon the sample analysis. Unlike Point estimate, we don’t want to find an exact value for the unknown population parameters, instead, we want to know the range that parameter can take at a certain level of probability. Thus, confidence intervals are designed to contain the parameter’s value based upon a stated probability.
The interpretation of a 95% confidence interval (Left side limit, Right side limit) means that there is a 95% chance that the population parameter will lie between the Left side limit and the Right side limit. The limit values of the confidence intervals are also called Critical Values .
5. Rare Event Rule: This rule is a quintessential property that allows us to make inferences about the population by using sample data. The rare event rule simply states that if we make an assumption about an event and find that the probability of that observed event is very small, then our assumption is false.
“If, under a given assumption, the probability of a particular observed event is exceptionally small, we conclude that the assumption is probably not correct.”
The basic idea here is that we test a Hypothesis claim by contrasting between two different things:
So we use the knowledge from the Rule of Rare events to accept or reject the original assumption while doing the Hypothesis testing. This rule forms the basis for the Test of Significance.
6. Test of Significance: This is a formal procedure used to check whether the observed data aligns with our assumed value or claimed value. We use p- values to examine whether we can reject the Null Hypothesis or not by comparing it with the test statistic derived from the sample data. In this test, we take a certain level of significance at the start and test our claim with respect to that particular level of significance only.
7. Test Statistic : A test statistic is a value that is derived from a sample statistic. We convert the sample statistic value into a distribution score such as Z score (Normal Distribution), t- score (T- distribution), or Chi-score (Chi-square distribution). If the score value lies in the confidence interval of the sample distribution then we fail to reject the null hypothesis, else we reject the null hypothesis.
8. P-Value: The P in this value stands for Probability Value. The P-Value is the probability of getting a value of the test statistic that is considered to be as extreme as the one representing the sample data while assuming that the null hypothesis is true. If the P-Value is small enough then we say that the results are statistically significant. The method of calculating the p-value changes depending upon the distribution of the sample. However, you can quickly calculate all the p values using the link mentioned below.
This is a set of very simple calculators that generate p-values from various test scores (i.e., t-test, chi-square….
www.socscistatistics.com
We all can agree that life is hard. Some people have to be truly extraordinary to be accepted by society whereas some just get it by sheer luck. Well, the same is the case when we talk about hypotheses. The Null Hypothesis always gets the benefit of the doubt and the Alternate Hypothesis has to showcase truly exceptional results in order to be accepted by statisticians. I can’t help but wonder if hypotheses were a real person how would the alternate Hypothesis look at the Null Hypothesis.
Since we are familiar with the dynamics of the relationship between null and alternate Hypotheses, let’s formally understand both of them.
2. Alternate Hypothesis: An alternate hypothesis is an actual claim that we want to test against the general information available on population parameters. An alternate Hypothesis is a statement which states that the value of the parameter is different from the one specified in the Null Hypothesis. In the world of Statistics, Rejection of null Hypothesis invariably means acceptance of Alternate Hypothesis. Let us understand the meaning of rejection of the Null Hypothesis with an example shown in the video below.
In order to do hypothesis testing, We will use the following steps:-
Step 1: Read the question and understand which parameters are used for analysis. It can be mean (μ), variance(σ), or proportion (p^).
Step 2: formulate the null Hypothesis based upon the target parameter to be studied in the problem.
Step 3: While forming the alternate hypothesis, figure out the type of tail which will be studied in the test.
Step 4: Check from the table below to identify which test to use based upon the target parameter which is to be tested.
Step 5: Now after choosing the test you must also decide the level of significance(α) and the level of confidence(1- α) for your test.
Step 6: Now check out the formulas mentioned below to calculate the test statistic from the available values of the parameter.
Step 7: After Calculating the test statistic’s value you can use two methods to analyze your results.
Just like any other human activity, hypothesis testing also involves a certain degree of errors that arise from the test of significance. Predominantly there are two kinds of errors that are most prevalent in hypothesis testing.
This was all for today’s brief introduction to the theory of Hypothesis testing. We will conduct an example problem based upon Kellogg's corn hypothesis that we discussed at the start of our discussion in the next blog. Stay tuned for the next blog and Take care!
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All research studies involve the use of the scientific method, which is a mathematical and experimental technique used to conduct experiments by developing and testing a hypothesis or a prediction about an outcome. Simply put, a hypothesis is a suggested solution to a problem. It includes elements that are expressed in terms of relationships with each other to explain a condition or an assumption that hasn’t been verified using facts. 1 The typical steps in a scientific method include developing such a hypothesis, testing it through various methods, and then modifying it based on the outcomes of the experiments.
A research hypothesis can be defined as a specific, testable prediction about the anticipated results of a study. 2 Hypotheses help guide the research process and supplement the aim of the study. After several rounds of testing, hypotheses can help develop scientific theories. 3 Hypotheses are often written as if-then statements.
Here are two hypothesis examples:
Dandelions growing in nitrogen-rich soils for two weeks develop larger leaves than those in nitrogen-poor soils because nitrogen stimulates vegetative growth. 4
If a company offers flexible work hours, then their employees will be happier at work. 5
A hypothesis expresses an expected relationship between variables in a study and is developed before conducting any research. Hypotheses are not opinions but rather are expected relationships based on facts and observations. They help support scientific research and expand existing knowledge. An incorrectly formulated hypothesis can affect the entire experiment leading to errors in the results so it’s important to know how to formulate a hypothesis and develop it carefully.
A few sources of a hypothesis include observations from prior studies, current research and experiences, competitors, scientific theories, and general conditions that can influence people. Figure 1 depicts the different steps in a research design and shows where exactly in the process a hypothesis is developed. 4
There are seven different types of hypotheses—simple, complex, directional, nondirectional, associative and causal, null, and alternative.
The seven types of hypotheses are listed below: 5 , 6,7
Example: Exercising in the morning every day will increase your productivity.
Example: Spending three hours or more on social media daily will negatively affect children’s mental health and productivity, more than that of adults.
Example: The inclusion of intervention X decreases infant mortality compared to the original treatment.
Example: Cats and dogs differ in the amount of affection they express.
Example: There is a positive association between physical activity levels and overall health.
A causal hypothesis, on the other hand, expresses a cause-and-effect association between variables.
Example: Long-term alcohol use causes liver damage.
Example: Sleep duration does not have any effect on productivity.
Example: Sleep duration affects productivity.
So, what makes a good hypothesis? Here are some important characteristics of a hypothesis. 8,9
The following list mentions some important functions of a hypothesis: 1
To summarize, a hypothesis provides the conceptual elements that complete the known data, conceptual relationships that systematize unordered elements, and conceptual meanings and interpretations that explain the unknown phenomena. 1
Listed below are the main steps explaining how to write a hypothesis. 2,4,5
For example, if you notice that an office’s vending machine frequently runs out of a specific snack, you may predict that more people in the office choose that snack over another.
For example, after observing employees’ break times at work, you could ask “why do more employees take breaks in the morning rather than in the afternoon?”
For example, based on your observations you might state a hypothesis that employees work more efficiently when the air conditioning in the office is set at a lower temperature. However, during your preliminary research you find that this hypothesis was proven incorrect by a prior study.
P opulation: The specific group or individual who is the main subject of the research
I nterest: The main concern of the study/research question
C omparison: The main alternative group
O utcome: The expected results
T ime: Duration of the experiment
Once you’ve finalized your hypothesis statement you would need to conduct experiments to test whether the hypothesis is true or false.
The following table provides examples of different types of hypotheses. 10 ,11
Null | Hyperactivity is not related to eating sugar. |
There is no relationship between height and shoe size. | |
Alternative | Hyperactivity is positively related to eating sugar. |
There is a positive association between height and shoe size. | |
Simple | Students who eat breakfast perform better in exams than students who don’t eat breakfast. |
Reduced screen time improves sleep quality. | |
Complex | People with high-sugar diet and sedentary activity levels are more likely to develop depression. |
Motorists who talk on the phone while driving will be more likely to make errors on a driving course than those who do not talk on the phone. | |
Directional | As job satisfaction increases, the rate of employee turnover decreases. |
Increase in sun exposure increases the risk of skin cancer. | |
Non-directional | College students will perform differently from elementary school students on a memory task. |
Advertising exposure correlates with variations in purchase decisions among consumers. | |
Associative | Hospitals have more sick people in them than other institutions in society. |
Watching TV is related to increased snacking. | |
Causal | Inadequate sleep decreases memory retention. |
Recreational drugs cause psychosis. |
Key takeaways
Here’s a summary of all the key points discussed in this article about how to write a hypothesis.
Hypotheses and research questions have different objectives and structure. The following table lists some major differences between the two. 9
Includes a prediction based on the proposed research | No prediction is made |
Designed to forecast the relationship of and between two or more variables | Variables may be explored |
Closed ended | Open ended, invites discussion |
Used if the research topic is well established and there is certainty about the relationship between the variables | Used for new topics that haven’t been researched extensively. The relationship between different variables is less known |
Here are a few examples to differentiate between a research question and hypothesis.
What is the effect of eating an apple a day by adults aged over 60 years on the frequency of physician visits? | Eating an apple each day, after the age of 60, will result in a reduction of frequency of physician visits |
What is the effect of flexible or fixed working hours on employee job satisfaction? | Workplaces that offer flexible working hours report higher levels of employee job satisfaction than workplaces with fixed hours. |
Does drinking coffee in the morning affect employees’ productivity? | Drinking coffee in the morning improves employees’ productivity. |
Yes, here’s a simple checklist to help you gauge the effectiveness of your hypothesis. 9 1. When writing a hypothesis statement, check if it: 2. Predicts the relationship between the stated variables and the expected outcome. 3. Uses simple and concise language and is not wordy. 4. Does not assume readers’ knowledge about the subject. 5. Has observable, falsifiable, and testable results.
As mentioned earlier in this article, a hypothesis is an assumption or prediction about an association between variables based on observations and simple evidence. These statements are usually generic. Research objectives, on the other hand, are more specific and dictated by hypotheses. The same hypothesis can be tested using different methods and the research objectives could be different in each case. For example, Louis Pasteur observed that food lasts longer at higher altitudes, reasoned that it could be because the air at higher altitudes is cleaner (with fewer or no germs), and tested the hypothesis by exposing food to air cleaned in the laboratory. 12 Thus, a hypothesis is predictive—if the reasoning is correct, X will lead to Y—and research objectives are developed to test these predictions.
Null hypothesis testing is a method to decide between two assumptions or predictions between variables (null and alternative hypotheses) in a statistical relationship in a sample. The null hypothesis, denoted as H 0 , claims that no relationship exists between variables in a population and any relationship in the sample reflects a sampling error or occurrence by chance. The alternative hypothesis, denoted as H 1 , claims that there is a relationship in the population. In every study, researchers need to decide whether the relationship in a sample occurred by chance or reflects a relationship in the population. This is done by hypothesis testing using the following steps: 13 1. Assume that the null hypothesis is true. 2. Determine how likely the sample relationship would be if the null hypothesis were true. This probability is called the p value. 3. If the sample relationship would be extremely unlikely, reject the null hypothesis and accept the alternative hypothesis. If the relationship would not be unlikely, accept the null hypothesis.
To summarize, researchers should know how to write a good hypothesis to ensure that their research progresses in the required direction. A hypothesis is a testable prediction about any behavior or relationship between variables, usually based on facts and observation, and states an expected outcome.
We hope this article has provided you with essential insight into the different types of hypotheses and their functions so that you can use them appropriately in your next research project.
References
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Learning Objectives
We finish our discussion of the hypothesis test for a population mean with a review of the meaning of the P-value, along with a review of type I and type II errors.
At this point, we assume you know how to use a P-value to make a decision in a hypothesis test. The logic is always the same. If we pick a level of significance (α), then we compare the P-value to α.
In fact, we find that we treat these as “rules” and apply them without thinking about what the P-value means. So let’s pause here and review the meaning of the P-value, since it is the connection between probability and decision-making in inference.
Let’s return to the familiar context of birth weights for babies in a town. Suppose that babies in the town had a mean birth weight of 3,500 grams in 2010. This year, a random sample of 50 babies has a mean weight of about 3,400 grams with a standard deviation of about 500 grams. Here is the distribution of birth weights in the sample.
Obviously, this sample weighs less on average than the population of babies in the town in 2010. A decrease in the town’s mean birth weight could indicate a decline in overall health of the town. But does this sample give strong evidence that the town’s mean birth weight is less than 3,500 grams this year?
We now know how to answer this question with a hypothesis test. Let’s use a significance level of 5%.
Let μ = mean birth weight in the town this year. The null hypothesis says there is “no change from 2010.”
Since the sample is large, we can conduct the T-test (without worrying about the shape of the distribution of birth weights for individual babies.)
Statistical software tells us the P-value is 0.082 = 8.2%. Since the P-value is greater than 0.05, we fail to reject the null hypothesis.
Our conclusion: This sample does not suggest that the mean birth weight this year is less than 3,500 grams ( P -value = 0.082). The sample from this year has a mean of 3,400 grams, which is 100 grams lower than the mean in 2010. But this difference is not statistically significant. It can be explained by the chance fluctuation we expect to see in random sampling.
A simulation can help us understand the P-value. In a simulation, we assume that the population mean is 3,500 grams. This is the null hypothesis. We assume the null hypothesis is true and select 1,000 random samples from a population with a mean of 3,500 grams. The mean of the sampling distribution is at 3,500 (as predicted by the null hypothesis.) We see this in the simulated sampling distribution.
In the simulation, we can see that about 8.6% of the samples have a mean less than 3,400. Since probability is the relative frequency of an event in the long run, we say there is an 8.6% chance that a random sample of 500 babies has a mean less than 3,400 if the population mean is 3,500. We can see that the corresponding area to the left of T = −1.41 in the T-model (with df = 49) also gives us a good estimate of the probability. This area is the P-value, about 8.2%.
If we generalize this statement, we say the P-value is the probability that random samples have results more extreme than the data if the null hypothesis is true. (By more extreme, we mean further from value of the parameter, in the direction of the alternative hypothesis.) We can also describe the P-value in terms of T-scores. The P-value is the probability that the test statistic from a random sample has a value more extreme than that associated with the data if the null hypothesis is true.
Do women who smoke run the risk of shorter pregnancy and premature birth? The mean pregnancy length is 266 days. We test the following hypotheses.
Suppose a random sample of 40 women who smoke during their pregnancy have a mean pregnancy length of 260 days with a standard deviation of 21 days. The P-value is 0.04.
What probability does the P-value of 0.04 describe? Label each of the following interpretations as valid or invalid.
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We know that statistical inference is based on probability, so there is always some chance of making a wrong decision. Recall that there are two types of wrong decisions that can be made in hypothesis testing. When we reject a null hypothesis that is true, we commit a type I error. When we fail to reject a null hypothesis that is false, we commit a type II error.
The following table summarizes the logic behind type I and type II errors.
It is possible to have some influence over the likelihoods of committing these errors. But decreasing the chance of a type I error increases the chance of a type II error. We have to decide which error is more serious for a given situation. Sometimes a type I error is more serious. Other times a type II error is more serious. Sometimes neither is serious.
Recall that if the null hypothesis is true, the probability of committing a type I error is α. Why is this? Well, when we choose a level of significance (α), we are choosing a benchmark for rejecting the null hypothesis. If the null hypothesis is true, then the probability that we will reject a true null hypothesis is α. So the smaller α is, the smaller the probability of a type I error.
It is more complicated to calculate the probability of a type II error. The best way to reduce the probability of a type II error is to increase the sample size. But once the sample size is set, larger values of α will decrease the probability of a type II error (while increasing the probability of a type I error).
General Guidelines for Choosing a Level of Significance
Let’s return to the investigation of the impact of smoking on pregnancy length.
Recap of the hypothesis test: The mean human pregnancy length is 266 days. We test the following hypotheses.
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In this “Hypothesis Test for a Population Mean,” we looked at the four steps of a hypothesis test as they relate to a claim about a population mean.
Since the hypothesis test is based on probability, random selection or assignment is essential in data production. Additionally, we need to check whether the t-model is a good fit for the sampling distribution of sample means. To use the t-model, the variable must be normally distributed in the population or the sample size must be more than 30. In practice, it is often impossible to verify that the variable is normally distributed in the population. If this is the case and the sample size is not more than 30, researchers often use the t-model if the sample is not strongly skewed and does not have outliers.
The logic of the hypothesis test is always the same. To state a conclusion about H 0 , we compare the P-value to the significance level, α.
A claim is a formal request for compensation, reimbursement, or acknowledgment of a right. It often involves submitting relevant documentation to support the demand. For instance, a Payment Claim is submitted to receive due payment for services rendered, while an Authorization Letter to Claim grants permission for another person to claim on behalf of the rightful owner. In specialized fields, a Construction Claim addresses disputes or additional costs in building projects, and an Insurance Claim seeks financial recovery for losses covered under an insurance policy.
A claim is a formal request for compensation, reimbursement, or acknowledgment of a right, often supported by relevant documentation. It is commonly used in various contexts such as payments, insurance, and legal disputes.
Claim : A claim is the main argument or thesis statement of a piece of writing. It is the writer’s position on a particular topic or issue. The claim should be specific, debatable, and clearly stated.
Example: Claim: “School uniforms improve student behavior and academic performance.”
Reason : A reason explains why the claim is valid. It provides the rationale behind the claim and shows why the reader should accept it. Reasons should be logical and directly support the claim.
Example: Reason: “Uniforms create a sense of equality among students, reducing peer pressure and distractions.”
Evidence : Evidence consists of facts, statistics, examples, expert opinions, or other data that support the reason. It provides concrete proof that the reason is valid and, consequently, that the claim is true.
Example: Evidence: “A study conducted by XYZ University found that schools with uniform policies saw a 20% decrease in disciplinary issues and a 15% increase in test scores.”
A claim of policy is a statement that advocates for a specific course of action or change in policy. It suggests that certain actions should be taken to address a problem or improve a situation. This type of claim often includes a proposal for a solution and is typically supported by evidence showing why the proposed action is necessary and beneficial.
The introduction sets the stage for your essay. It should:
“In today’s digital age, the use of social media has become ubiquitous. While it offers numerous benefits, there is a growing concern about its impact on mental health. This essay will argue that excessive social media use leads to increased anxiety and depression among teenagers.”
The thesis statement clearly states your main argument. It should be concise and specific.
“Excessive use of social media contributes to heightened anxiety and depression among teenagers.”
Each body paragraph should focus on one main idea that supports your thesis. Include evidence such as statistics, quotes, studies, and real-life examples.
Paragraph 1:
Paragraph 2:
Paragraph 3:
Addressing counterarguments strengthens your essay by showing you have considered multiple viewpoints.
Counterargument: Some argue that social media helps teenagers build social connections and support networks.
Rebuttal: While social media can facilitate connections, it often leads to superficial relationships. Moreover, the negative effects on mental health outweigh the potential benefits of these connections.
The conclusion should summarize your main points and restate the thesis in light of the evidence presented. It should also provide a final thought or call to action.
A claim is the main argument or stance you take on a particular issue in your essay.
State your claim clearly and concisely in the thesis statement of your introduction.
No, a claim should be a declarative statement, not a question.
Generally, one main claim is supported by several smaller, supporting claims.
A strong claim is specific, debatable, and backed by evidence.
No, a claim should be an argument that requires support and evidence, not a universally accepted fact.
Yes, addressing counterclaims strengthens your argument by showing consideration of opposing views.
Yes, refining your claim as you gather more evidence and insights is common.
A claim is the main argument of the essay, while a topic sentence introduces the main idea of a paragraph.
Ensure your claim presents a viewpoint that others might dispute or have differing opinions on.
Text prompt
10 Examples of Public speaking
20 Examples of Gas lighting
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Present the findings in your results and discussion section. Though the specific details might vary, the procedure you will use when testing a hypothesis will always follow some version of these steps. Table of contents. Step 1: State your null and alternate hypothesis. Step 2: Collect data. Step 3: Perform a statistical test.
The alternative hypothesis (H a) is the other answer to your research question. It claims that there's an effect in the population. Often, your alternative hypothesis is the same as your research hypothesis. In other words, it's the claim that you expect or hope will be true. The alternative hypothesis is the complement to the null hypothesis.
This page contains two hypothesis testing examples for one sample z-tests. One Sample Hypothesis Testing Example: One Tailed Z Test. A principal at a certain school claims that the students in his school are above average intelligence. A random sample of thirty students IQ scores have a mean score of 112.5. Is there sufficient evidence to ...
If the biologist set her significance level \(\alpha\) at 0.05 and used the critical value approach to conduct her hypothesis test, she would reject the null hypothesis if her test statistic t* were less than -1.6939 (determined using statistical software or a t-table):s-3-3. Since the biologist's test statistic, t* = -4.60, is less than -1.6939, the biologist rejects the null hypothesis.
Developing a hypothesis (with example) Step 1. Ask a question. Writing a hypothesis begins with a research question that you want to answer. The question should be focused, specific, and researchable within the constraints of your project. Example: Research question.
A teacher believes that 85% of students in the class will want to go on a field trip to the local zoo. The teacher performs a hypothesis test to determine if the percentage is the same or different from 85%. The teacher samples 50 students and 39 reply that they would want to go to the zoo. For the hypothesis test, use a 1% level of significance.
Conduct a hypothesis test using test statistics and \(p\)-values with a preset \(\alpha = 0.05\). Answer. Set up the Hypothesis Test: Since the problem is about a mean, this is a test of a single population mean. Set the null and alternative hypothesis: In this case there is an implied challenge or claim.
The alternative hypothesis, H1 , is the competing claim suggesting an effect or a difference. Statistical tests determine whether to reject the null hypothesis in favor of the alternative hypothesis based on the data. ... For example, a simple hypothesis might state, "Increased sunlight exposure increases the growth rate of sunflowers." Here ...
Unit 12: Significance tests (hypothesis testing) Significance tests give us a formal process for using sample data to evaluate the likelihood of some claim about a population value. Learn how to conduct significance tests and calculate p-values to see how likely a sample result is to occur by random chance. You'll also see how we use p-values ...
9.6: Additional Information and Full Hypothesis Test Examples. For each of the word problems, use a solution sheet to do the hypothesis test. The solution sheet is found in . Please feel free to make copies of the solution sheets. ... A particular brand of tires claims that its deluxe tire averages at least 50,000 miles before it needs to be ...
A hypothesis is a tentative statement about the relationship between two or more variables. It is a specific, testable prediction about what you expect to happen in a study. It is a preliminary answer to your question that helps guide the research process. Consider a study designed to examine the relationship between sleep deprivation and test ...
There is sufficient evidence to support the claim that… Or, we would write: We fail to reject the null hypothesis at the 5% significance level. There is not sufficient evidence to support the claim that… The following examples show how to write a hypothesis test conclusion in both scenarios. Example 1: Reject the Null Hypothesis Conclusion
10.1 - Setting the Hypotheses: Examples. A significance test examines whether the null hypothesis provides a plausible explanation of the data. The null hypothesis itself does not involve the data. It is a statement about a parameter (a numerical characteristic of the population). These population values might be proportions or means or ...
Statistics: Hypothesis Testing . A hypothesis is a claim made about a population. A hypothesis test uses sample data to test the validity of the claim. This handout will define the basic elements of hypothesis testing and provide the steps to perform hypothesis tests using the P-value method and the critical value method.
For the hypothesis test, use a 1% level of significance. Example 9.5.12. Suppose a consumer group suspects that the proportion of households that have three or more cell phones is 30%. A cell phone company has reason to believe that the proportion is not 30%.
Example 8.4.7. Joon believes that 50% of first-time brides in the United States are younger than their grooms. She performs a hypothesis test to determine if the percentage is the same or different from 50%. Joon samples 100 first-time brides and 53 reply that they are younger than their grooms.
Step 1: Define the Hypothesis. Usually, the reported value (or the claim statistics) is stated as the hypothesis and presumed to be true. For the above examples, the hypothesis will be: Example A ...
Example 1: Biology. Hypothesis tests are often used in biology to determine whether some new treatment, fertilizer, pesticide, chemical, etc. causes increased growth, stamina, immunity, etc. in plants or animals. For example, suppose a biologist believes that a certain fertilizer will cause plants to grow more during a one-month period than ...
STA 2023 & 2122. The first thing needed to know is that there are two Hypotheses called the Null Hypothesis (H0) and the Alternative Hypothesis (H1); they are mutually exclusive. There is also a claim, which is something that can be said or inferred to the Population Proportion or the Population Mean. This claim can be that the proportion has ...
Review. In a hypothesis test, sample data is evaluated in order to arrive at a decision about some type of claim.If certain conditions about the sample are satisfied, then the claim can be evaluated for a population. In a hypothesis test, we: Evaluate the null hypothesis, typically denoted with \(H_{0}\).The null is not rejected unless the hypothesis test shows otherwise.
Null Hypothesis: A null hypothesis is an initial claim or a generally accepted fact about the population. The null hypothesis is basically a statement which states that the value of the population ...
Example: Long-term alcohol use causes liver damage. Null: Claims that the original hypothesis is false by showing that there is no relationship between the variables. Example: Sleep duration does not have any effect on productivity. Alternative: States the opposite of the null hypothesis, that is, a relationship exists between two variables.
The hypotheses are claims about the population mean, µ. The null hypothesis is a hypothesis that the mean equals a specific value, µ 0. The alternative hypothesis is the competing claim that µ is less than, greater than, or not equal to the . When is < or > , the test is a one-tailed test. When is ≠ , the test is a two-tailed test.
A claim is a formal request for compensation, reimbursement, or acknowledgment of a right, often supported by relevant documentation. It is commonly used in various contexts such as payments, insurance, and legal disputes. Examples of Claim. Payment Claim - Requesting payment for completed work or services rendered.