## Z-test Calculator

Table of contents

This Z-test calculator is a tool that helps you perform a one-sample Z-test on the population's mean . Two forms of this test - a two-tailed Z-test and a one-tailed Z-tests - exist, and can be used depending on your needs. You can also choose whether the calculator should determine the p-value from Z-test or you'd rather use the critical value approach!

Read on to learn more about Z-test in statistics, and, in particular, when to use Z-tests, what is the Z-test formula, and whether to use Z-test vs. t-test. As a bonus, we give some step-by-step examples of how to perform Z-tests!

Or you may also check our t-statistic calculator , where you can learn the concept of another essential statistic. If you are also interested in F-test, check our F-statistic calculator .

## What is a Z-test?

A one sample Z-test is one of the most popular location tests. The null hypothesis is that the population mean value is equal to a given number, μ 0 \mu_0 μ 0 :

We perform a two-tailed Z-test if we want to test whether the population mean is not μ 0 \mu_0 μ 0 :

and a one-tailed Z-test if we want to test whether the population mean is less/greater than μ 0 \mu_0 μ 0 :

Let us now discuss the assumptions of a one-sample Z-test.

## When do I use Z-tests?

You may use a Z-test if your sample consists of independent data points and:

the data is normally distributed , and you know the population variance ;

the sample is large , and data follows a distribution which has a finite mean and variance. You don't need to know the population variance.

The reason these two possibilities exist is that we want the test statistics that follow the standard normal distribution N ( 0 , 1 ) \mathrm N(0, 1) N ( 0 , 1 ) . In the former case, it is an exact standard normal distribution, while in the latter, it is approximately so, thanks to the central limit theorem.

The question remains, "When is my sample considered large?" Well, there's no universal criterion. In general, the more data points you have, the better the approximation works. Statistics textbooks recommend having no fewer than 50 data points, while 30 is considered the bare minimum.

## Z-test formula

Let x 1 , . . . , x n x_1, ..., x_n x 1 , ... , x n be an independent sample following the normal distribution N ( μ , σ 2 ) \mathrm N(\mu, \sigma^2) N ( μ , σ 2 ) , i.e., with a mean equal to μ \mu μ , and variance equal to σ 2 \sigma ^2 σ 2 .

We pose the null hypothesis, H 0 : μ = μ 0 \mathrm H_0 \!\!:\!\! \mu = \mu_0 H 0 : μ = μ 0 .

We define the test statistic, Z , as:

x ˉ \bar x x ˉ is the sample mean, i.e., x ˉ = ( x 1 + . . . + x n ) / n \bar x = (x_1 + ... + x_n) / n x ˉ = ( x 1 + ... + x n ) / n ;

μ 0 \mu_0 μ 0 is the mean postulated in H 0 \mathrm H_0 H 0 ;

n n n is sample size; and

σ \sigma σ is the population standard deviation.

In what follows, the uppercase Z Z Z stands for the test statistic (treated as a random variable), while the lowercase z z z will denote an actual value of Z Z Z , computed for a given sample drawn from N(μ,σ²).

If H 0 \mathrm H_0 H 0 holds, then the sum S n = x 1 + . . . + x n S_n = x_1 + ... + x_n S n = x 1 + ... + x n follows the normal distribution, with mean n μ 0 n \mu_0 n μ 0 and variance n 2 σ n^2 \sigma n 2 σ . As Z Z Z is the standardization (z-score) of S n / n S_n/n S n / n , we can conclude that the test statistic Z Z Z follows the standard normal distribution N ( 0 , 1 ) \mathrm N(0, 1) N ( 0 , 1 ) , provided that H 0 \mathrm H_0 H 0 is true. By the way, we have the z-score calculator if you want to focus on this value alone.

If our data does not follow a normal distribution, or if the population standard deviation is unknown (and thus in the formula for Z Z Z we substitute the population standard deviation σ \sigma σ with sample standard deviation), then the test statistics Z Z Z is not necessarily normal. However, if the sample is sufficiently large, then the central limit theorem guarantees that Z Z Z is approximately N ( 0 , 1 ) \mathrm N(0, 1) N ( 0 , 1 ) .

In the sections below, we will explain to you how to use the value of the test statistic, z z z , to make a decision , whether or not you should reject the null hypothesis . Two approaches can be used in order to arrive at that decision: the p-value approach, and critical value approach - and we cover both of them! Which one should you use? In the past, the critical value approach was more popular because it was difficult to calculate p-value from Z-test. However, with help of modern computers, we can do it fairly easily, and with decent precision. In general, you are strongly advised to report the p-value of your tests!

## p-value from Z-test

Formally, the p-value is the smallest level of significance at which the null hypothesis could be rejected. More intuitively, p-value answers the questions: provided that I live in a world where the null hypothesis holds, how probable is it that the value of the test statistic will be at least as extreme as the z z z - value I've got for my sample? Hence, a small p-value means that your result is very improbable under the null hypothesis, and so there is strong evidence against the null hypothesis - the smaller the p-value, the stronger the evidence.

To find the p-value, you have to calculate the probability that the test statistic, Z Z Z , is at least as extreme as the value we've actually observed, z z z , provided that the null hypothesis is true. (The probability of an event calculated under the assumption that H 0 \mathrm H_0 H 0 is true will be denoted as P r ( event ∣ H 0 ) \small \mathrm{Pr}(\text{event} | \mathrm{H_0}) Pr ( event ∣ H 0 ) .) It is the alternative hypothesis which determines what more extreme means :

- Two-tailed Z-test: extreme values are those whose absolute value exceeds ∣ z ∣ |z| ∣ z ∣ , so those smaller than − ∣ z ∣ -|z| − ∣ z ∣ or greater than ∣ z ∣ |z| ∣ z ∣ . Therefore, we have:

The symmetry of the normal distribution gives:

- Left-tailed Z-test: extreme values are those smaller than z z z , so
- Right-tailed Z-test: extreme values are those greater than z z z , so

To compute these probabilities, we can use the cumulative distribution function, (cdf) of N ( 0 , 1 ) \mathrm N(0, 1) N ( 0 , 1 ) , which for a real number, x x x , is defined as:

Also, p-values can be nicely depicted as the area under the probability density function (pdf) of N ( 0 , 1 ) \mathrm N(0, 1) N ( 0 , 1 ) , due to:

## Two-tailed Z-test and one-tailed Z-test

With all the knowledge you've got from the previous section, you're ready to learn about Z-tests.

- Two-tailed Z-test:

From the fact that Φ ( − z ) = 1 − Φ ( z ) \Phi(-z) = 1 - \Phi(z) Φ ( − z ) = 1 − Φ ( z ) , we deduce that

The p-value is the area under the probability distribution function (pdf) both to the left of − ∣ z ∣ -|z| − ∣ z ∣ , and to the right of ∣ z ∣ |z| ∣ z ∣ :

- Left-tailed Z-test:

The p-value is the area under the pdf to the left of our z z z :

- Right-tailed Z-test:

The p-value is the area under the pdf to the right of z z z :

The decision as to whether or not you should reject the null hypothesis can be now made at any significance level, α \alpha α , you desire!

if the p-value is less than, or equal to, α \alpha α , the null hypothesis is rejected at this significance level; and

if the p-value is greater than α \alpha α , then there is not enough evidence to reject the null hypothesis at this significance level.

## Z-test critical values & critical regions

The critical value approach involves comparing the value of the test statistic obtained for our sample, z z z , to the so-called critical values . These values constitute the boundaries of regions where the test statistic is highly improbable to lie . Those regions are often referred to as the critical regions , or rejection regions . The decision of whether or not you should reject the null hypothesis is then based on whether or not our z z z belongs to the critical region.

The critical regions depend on a significance level, α \alpha α , of the test, and on the alternative hypothesis. The choice of α \alpha α is arbitrary; in practice, the values of 0.1, 0.05, or 0.01 are most commonly used as α \alpha α .

Once we agree on the value of α \alpha α , we can easily determine the critical regions of the Z-test:

To decide the fate of H 0 \mathrm H_0 H 0 , check whether or not your z z z falls in the critical region:

If yes, then reject H 0 \mathrm H_0 H 0 and accept H 1 \mathrm H_1 H 1 ; and

If no, then there is not enough evidence to reject H 0 \mathrm H_0 H 0 .

As you see, the formulae for the critical values of Z-tests involve the inverse, Φ − 1 \Phi^{-1} Φ − 1 , of the cumulative distribution function (cdf) of N ( 0 , 1 ) \mathrm N(0, 1) N ( 0 , 1 ) .

## How to use the one-sample Z-test calculator?

Our calculator reduces all the complicated steps:

Choose the alternative hypothesis: two-tailed or left/right-tailed.

In our Z-test calculator, you can decide whether to use the p-value or critical regions approach. In the latter case, set the significance level, α \alpha α .

Enter the value of the test statistic, z z z . If you don't know it, then you can enter some data that will allow us to calculate your z z z for you:

- sample mean x ˉ \bar x x ˉ (If you have raw data, go to the average calculator to determine the mean);
- tested mean μ 0 \mu_0 μ 0 ;
- sample size n n n ; and
- population standard deviation σ \sigma σ (or sample standard deviation if your sample is large).

Results appear immediately below the calculator.

If you want to find z z z based on p-value , please remember that in the case of two-tailed tests there are two possible values of z z z : one positive and one negative, and they are opposite numbers. This Z-test calculator returns the positive value in such a case. In order to find the other possible value of z z z for a given p-value, just take the number opposite to the value of z z z displayed by the calculator.

## Z-test examples

To make sure that you've fully understood the essence of Z-test, let's go through some examples:

- A bottle filling machine follows a normal distribution. Its standard deviation, as declared by the manufacturer, is equal to 30 ml. A juice seller claims that the volume poured in each bottle is, on average, one liter, i.e., 1000 ml, but we suspect that in fact the average volume is smaller than that...

Formally, the hypotheses that we set are the following:

H 0 : μ = 1000 ml \mathrm H_0 \! : \mu = 1000 \text{ ml} H 0 : μ = 1000 ml

H 1 : μ < 1000 ml \mathrm H_1 \! : \mu \lt 1000 \text{ ml} H 1 : μ < 1000 ml

We went to a shop and bought a sample of 9 bottles. After carefully measuring the volume of juice in each bottle, we've obtained the following sample (in milliliters):

1020 , 970 , 1000 , 980 , 1010 , 930 , 950 , 980 , 980 \small 1020, 970, 1000, 980, 1010, 930, 950, 980, 980 1020 , 970 , 1000 , 980 , 1010 , 930 , 950 , 980 , 980 .

Sample size: n = 9 n = 9 n = 9 ;

Sample mean: x ˉ = 980 m l \bar x = 980 \ \mathrm{ml} x ˉ = 980 ml ;

Population standard deviation: σ = 30 m l \sigma = 30 \ \mathrm{ml} σ = 30 ml ;

And, therefore, p-value = Φ ( − 2 ) ≈ 0.0228 \text{p-value} = \Phi(-2) \approx 0.0228 p-value = Φ ( − 2 ) ≈ 0.0228 .

As 0.0228 < 0.05 0.0228 \lt 0.05 0.0228 < 0.05 , we conclude that our suspicions aren't groundless; at the most common significance level, 0.05, we would reject the producer's claim, H 0 \mathrm H_0 H 0 , and accept the alternative hypothesis, H 1 \mathrm H_1 H 1 .

We tossed a coin 50 times. We got 20 tails and 30 heads. Is there sufficient evidence to claim that the coin is biased?

Clearly, our data follows Bernoulli distribution, with some success probability p p p and variance σ 2 = p ( 1 − p ) \sigma^2 = p (1-p) σ 2 = p ( 1 − p ) . However, the sample is large, so we can safely perform a Z-test. We adopt the convention that getting tails is a success.

Let us state the null and alternative hypotheses:

H 0 : p = 0.5 \mathrm H_0 \! : p = 0.5 H 0 : p = 0.5 (the coin is fair - the probability of tails is 0.5 0.5 0.5 )

H 1 : p ≠ 0.5 \mathrm H_1 \! : p \ne 0.5 H 1 : p = 0.5 (the coin is biased - the probability of tails differs from 0.5 0.5 0.5 )

In our sample we have 20 successes (denoted by ones) and 30 failures (denoted by zeros), so:

Sample size n = 50 n = 50 n = 50 ;

Sample mean x ˉ = 20 / 50 = 0.4 \bar x = 20/50 = 0.4 x ˉ = 20/50 = 0.4 ;

Population standard deviation is given by σ = 0.5 × 0.5 \sigma = \sqrt{0.5 \times 0.5} σ = 0.5 × 0.5 (because 0.5 0.5 0.5 is the proportion p p p hypothesized in H 0 \mathrm H_0 H 0 ). Hence, σ = 0.5 \sigma = 0.5 σ = 0.5 ;

- And, therefore

Since 0.1573 > 0.1 0.1573 \gt 0.1 0.1573 > 0.1 we don't have enough evidence to reject the claim that the coin is fair , even at such a large significance level as 0.1 0.1 0.1 . In that case, you may safely toss it to your Witcher or use the coin flip probability calculator to find your chances of getting, e.g., 10 heads in a row (which are extremely low!).

## What is the difference between Z-test vs t-test?

We use a t-test for testing the population mean of a normally distributed dataset which had an unknown population standard deviation . We get this by replacing the population standard deviation in the Z-test statistic formula by the sample standard deviation, which means that this new test statistic follows (provided that H₀ holds) the t-Student distribution with n-1 degrees of freedom instead of N(0,1) .

## When should I use t-test over the Z-test?

For large samples, the t-Student distribution with n degrees of freedom approaches the N(0,1). Hence, as long as there are a sufficient number of data points (at least 30), it does not really matter whether you use the Z-test or the t-test, since the results will be almost identical. However, for small samples with unknown variance, remember to use the t-test instead of Z-test .

## How do I calculate the Z test statistic?

To calculate the Z test statistic:

- Compute the arithmetic mean of your sample .
- From this mean subtract the mean postulated in null hypothesis .
- Multiply by the square root of size sample .
- Divide by the population standard deviation .
- That's it, you've just computed the Z test statistic!

Here, we perform a Z-test for population mean μ. Null hypothesis H₀: μ = μ₀.

Alternative hypothesis H₁

Significance level α

The probability that we reject the true hypothesis H₀ (type I error).

## Hypothesis Testing Calculator

$H_o$: | |||

$H_a$: | μ | ≠ | μ₀ |

$n$ | = | $\bar{x}$ | = | = |

$\text{Test Statistic: }$ | = |

$\text{Degrees of Freedom: } $ | $df$ | = |

$ \text{Level of Significance: } $ | $\alpha$ | = |

## Type II Error

$H_o$: | $\mu$ | ||

$H_a$: | $\mu$ | ≠ | $\mu_0$ |

$n$ | = | σ | = | $\mu$ | = |

$\text{Level of Significance: }$ | $\alpha$ | = |

The first step in hypothesis testing is to calculate the test statistic. The formula for the test statistic depends on whether the population standard deviation (σ) is known or unknown. If σ is known, our hypothesis test is known as a z test and we use the z distribution. If σ is unknown, our hypothesis test is known as a t test and we use the t distribution. Use of the t distribution relies on the degrees of freedom, which is equal to the sample size minus one. Furthermore, if the population standard deviation σ is unknown, the sample standard deviation s is used instead. To switch from σ known to σ unknown, click on $\boxed{\sigma}$ and select $\boxed{s}$ in the Hypothesis Testing Calculator.

$\sigma$ Known | $\sigma$ Unknown | |

Test Statistic | $ z = \dfrac{\bar{x}-\mu_0}{\sigma/\sqrt{{\color{Black} n}}} $ | $ t = \dfrac{\bar{x}-\mu_0}{s/\sqrt{n}} $ |

Next, the test statistic is used to conduct the test using either the p-value approach or critical value approach. The particular steps taken in each approach largely depend on the form of the hypothesis test: lower tail, upper tail or two-tailed. The form can easily be identified by looking at the alternative hypothesis (H a ). If there is a less than sign in the alternative hypothesis then it is a lower tail test, greater than sign is an upper tail test and inequality is a two-tailed test. To switch from a lower tail test to an upper tail or two-tailed test, click on $\boxed{\geq}$ and select $\boxed{\leq}$ or $\boxed{=}$, respectively.

Lower Tail Test | Upper Tail Test | Two-Tailed Test |

$H_0 \colon \mu \geq \mu_0$ | $H_0 \colon \mu \leq \mu_0$ | $H_0 \colon \mu = \mu_0$ |

$H_a \colon \mu | $H_a \colon \mu \neq \mu_0$ |

In the p-value approach, the test statistic is used to calculate a p-value. If the test is a lower tail test, the p-value is the probability of getting a value for the test statistic at least as small as the value from the sample. If the test is an upper tail test, the p-value is the probability of getting a value for the test statistic at least as large as the value from the sample. In a two-tailed test, the p-value is the probability of getting a value for the test statistic at least as unlikely as the value from the sample.

To test the hypothesis in the p-value approach, compare the p-value to the level of significance. If the p-value is less than or equal to the level of signifance, reject the null hypothesis. If the p-value is greater than the level of significance, do not reject the null hypothesis. This method remains unchanged regardless of whether it's a lower tail, upper tail or two-tailed test. To change the level of significance, click on $\boxed{.05}$. Note that if the test statistic is given, you can calculate the p-value from the test statistic by clicking on the switch symbol twice.

In the critical value approach, the level of significance ($\alpha$) is used to calculate the critical value. In a lower tail test, the critical value is the value of the test statistic providing an area of $\alpha$ in the lower tail of the sampling distribution of the test statistic. In an upper tail test, the critical value is the value of the test statistic providing an area of $\alpha$ in the upper tail of the sampling distribution of the test statistic. In a two-tailed test, the critical values are the values of the test statistic providing areas of $\alpha / 2$ in the lower and upper tail of the sampling distribution of the test statistic.

To test the hypothesis in the critical value approach, compare the critical value to the test statistic. Unlike the p-value approach, the method we use to decide whether to reject the null hypothesis depends on the form of the hypothesis test. In a lower tail test, if the test statistic is less than or equal to the critical value, reject the null hypothesis. In an upper tail test, if the test statistic is greater than or equal to the critical value, reject the null hypothesis. In a two-tailed test, if the test statistic is less than or equal the lower critical value or greater than or equal to the upper critical value, reject the null hypothesis.

Lower Tail Test | Upper Tail Test | Two-Tailed Test |

If $z \leq -z_\alpha$, reject $H_0$. | If $z \geq z_\alpha$, reject $H_0$. | If $z \leq -z_{\alpha/2}$ or $z \geq z_{\alpha/2}$, reject $H_0$. |

If $t \leq -t_\alpha$, reject $H_0$. | If $t \geq t_\alpha$, reject $H_0$. | If $t \leq -t_{\alpha/2}$ or $t \geq t_{\alpha/2}$, reject $H_0$. |

When conducting a hypothesis test, there is always a chance that you come to the wrong conclusion. There are two types of errors you can make: Type I Error and Type II Error. A Type I Error is committed if you reject the null hypothesis when the null hypothesis is true. Ideally, we'd like to accept the null hypothesis when the null hypothesis is true. A Type II Error is committed if you accept the null hypothesis when the alternative hypothesis is true. Ideally, we'd like to reject the null hypothesis when the alternative hypothesis is true.

Condition | ||||

$H_0$ True | $H_a$ True | |||

Conclusion | Accept $H_0$ | Correct | Type II Error | |

Reject $H_0$ | Type I Error | Correct |

Hypothesis testing is closely related to the statistical area of confidence intervals. If the hypothesized value of the population mean is outside of the confidence interval, we can reject the null hypothesis. Confidence intervals can be found using the Confidence Interval Calculator . The calculator on this page does hypothesis tests for one population mean. Sometimes we're interest in hypothesis tests about two population means. These can be solved using the Two Population Calculator . The probability of a Type II Error can be calculated by clicking on the link at the bottom of the page.

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We use a t-test for testing the population mean of a normally distributed dataset which had an unknown population standard deviation.We get this by replacing the population standard deviation in the Z-test statistic formula by the sample standard deviation, which means that this new test statistic follows (provided that H₀ holds) the t-Student distribution with n-1 degrees of freedom instead ...

Hypothesis Testing Calculator. The first step in hypothesis testing is to calculate the test statistic. The formula for the test statistic depends on whether the population standard deviation (σ) is known or unknown. If σ is known, our hypothesis test is known as a z test and we use the z distribution. If σ is unknown, our hypothesis test is ...

This Z-test calculator computes data for both one-sample and two-sample Z-tests. It also provides a diagram to show the position of the Z-score and the acceptance/rejection regions. ... statistical hypothesis tests are indispensable tools used to determine if evidence exists to reject a prevailing assumption or theory, known as the null ...

Use a Z test when you need to compare group means. Use the 1-sample analysis to determine whether a population mean is different from a hypothesized value. Or use the 2-sample version to determine whether two population means differ. A Z test is a form of inferential statistics. It uses samples to draw conclusions about populations.

The Z-test Calculator is a statistical tool designed to determine if there is a significant difference between sample and population means. It's ideal for researchers and students engaged in hypothesis testing and data analysis. Z-test Calculation Formula Explained

The main properties of a one sample z-test for one population mean are: Depending on our knowledge about the "no effect" situation, the z-test can be two-tailed, left-tailed or right-tailed. The main principle of hypothesis testing is that the null hypothesis is rejected if the test statistic obtained is sufficiently unlikely under the ...

z-test calculator. Natural Language; Math Input; Extended Keyboard Examples Upload Random. ... Input values. Null hypothesis. Alternative hypothesis. Test statistic. p ‐value. Sampling distribution of test statistic under the null hypothesis. Power function. Significance level 5%. Test conclusions. Assumptions.

Single Sample Z Score Calculator. This tool calculates the z -score of the mean of a single sample. It can be used to make a judgement about whether the sample differs significantly on some axis from the population from which it was originally drawn. By default, this tool works on the assumption that you already know the mean value of your ...

This section answers some common questions about . Use this Hypothesis Test Calculator for quick results in Python and R. Learn the step-by-step hypothesis test process and why hypothesis testing is important.

Please enter the value of p above, and then press "Calculate Z from P". Additional Z Statistic Calculators. If you're interested in using the z statistic for hypothesis testing, then we have a couple of other calculators that might help you. Z-Test Calculator for a Single Sample Z-Test Calculator for 2 Population Proportions

The below is the solved examples for Z-statistic calculation by using standard deviation & without using standard deviation. Z-test calculator, formulas & example work with steps to estimate z-statistic (Z0), critical value of normal distribution (Ze) & test of hypothesis (H0) for large sample mean, proportion & two means or proportions ...

Z-Hypothesis Testing (stats) | Desmos. Enter the size of the sample n, sample mean m, population standard deviation s. n = 1. m = 0. s = 1. Enter M_0, the value of the null hypothesis and click on the tab below corresponding to the proper form of the alternative hypothesis. Or click on confidence interval to obtain that (with CL=1-alpha) M0 = 0.

Z test online. Target: To check if the assumed μ 0 is statistically correct, based on a sample average. You know the standard deviation from previous researches. Example1: A farmer calculated last year the average of the apples' weight in his apple orchard μ 0 equals 17 kg, based on the entire population. The current year he checked a small sample of apples and the sample average x equals 18 kg

A one sample z-test is used to test whether or not the mean of a population is equal to some value when the population standard deviation is known. To perform a one sample z-test, simply fill in the information below and then click the "Calculate" button. Enter raw data Enter summary data.

This test is commonly used in hypothesis testing when you have a single set of data points and want to determine if it's representative of a larger population or if there's a significant difference between the sample and the population. Here's the formula for a One Sample Z-Test: Z = (X̄ - μ) / (σ / √ (n)) Where: Z is the Z-statistic.

A Z-test is a type of statistical hypothesis test where the test-statistic follows a normal distribution. The name Z-test comes from the Z-score of the normal distribution. This is a measure of how many standard deviations away a raw score or sample statistics is from the populations' mean. Z-tests are the most common statistical tests ...

Z-tests are crucial statistical procedures to test for claims about population parameters using the normal distribution. We can use for one population or two population means provided that the population standard deviations are known. Also, we can use a z-test to test for claims about a population proportion. Also, via the Central Limit Theorem, the...

Instructions: This calculator conducts a Z-test for two population means ( \mu_1 μ1 and \mu_2 μ2 ), with known population standard deviations ( \sigma_1 σ1 and \sigma_2 σ2 ). Please select the null and alternative hypotheses, type the significance level, the sample means, the population standard deviations, the sample sizes, and the results ...

The z-score associated with a 5% alpha level / 2 is 1.96.. Step 5: Compare the calculated z-score from Step 3 with the table z-score from Step 4. If the calculated z-score is larger, you can reject the null hypothesis. 8.99 > 1.96, so we can reject the null hypothesis.. Example 2: Suppose that in a survey of 700 women and 700 men, 35% of women and 30% of men indicated that they support a ...

Additional Z Statistic Calculators. If you're interested in using the z statistic for hypothesis testing and the like, then we have a number of other calculators that might help you. Z-Test Calculator for a Single Sample Z-Test Calculator for 2 Population Proportions Z Score Calculator for a Single Raw Value (Includes z from p)

What is Z-Test?. Z-Test is a statistical test which let's us approximate the distribution of the test statistic under the null hypothesis using normal distribution.. Z-Test is a test statistic commonly used in hypothesis test when the sample data is large.For carrying out the Z-Test, population parameters such as mean, variance, and standard deviation should be known.

Performing a Z-Test on the TI-83 Plus and TI-84 Plus. From the home screen, press STAT to select the TESTS menu. "Z-Test" should already be selected, so press ENTER to be taken to the Z-Test menu. Now select the desired settings and values. While it is possible to use a list to store a set of scores from which your calculator can determine ...

Instructions: This calculator conducts a Z-test for one population proportion (p). Please select the null and alternative hypotheses, type the hypothesized population proportion p_0 p0, the significance level \alpha α, the sample proportion or number o favorable cases, and the sample size, and the results of the z-test for one proportion will ...