One Tailed Z Test P Value Calculator

Calculator

Calculation mode

One tailed direction

Alpha level

Known z statistic

Sample mean

Hypothesized mean

Population standard deviation

Sample size for mean

Successes for proportion

Sample size for proportion

Hypothesized proportion

Advanced option

Apply proportion continuity correction

Formula Used

Known z statistic: use the entered z value directly.

Mean test: z = (x̄ - μ0) / (σ / √n)

Proportion test: z = (p̂ - p0) / √(p0(1 - p0) / n)

Right tailed p value: p = 1 - Φ(z)

Left tailed p value: p = Φ(z)

Decision rule: reject H0 when p value ≤ alpha.

How to Use This Calculator

Select whether you already know z, have mean data, or have proportion data.
Choose right tailed for a greater than claim.
Choose left tailed for a less than claim.
Enter alpha, usually 0.10, 0.05, or 0.01.
Fill only the fields needed for your selected method.
Press Calculate to view the p value and decision.
Use CSV or PDF buttons to export the same calculated result.

Example Data Table

Case	Mode	Tail	Inputs	Meaning
Quality score	Mean	Right	x̄ = 104, μ0 = 100, σ = 12, n = 36	Tests whether the average score increased.
Conversion rate	Proportion	Right	x = 68, n = 100, p0 = 0.60	Tests whether the success rate improved.
Known statistic	Z score	Left	z = -1.75, alpha = 0.05	Tests whether the result is unusually low.

One Tailed Z Test P Value Guide

Purpose

A one tailed z test asks whether evidence points in one chosen direction. It is used when the population standard deviation is known, or when a large sample supports normal approximation. This calculator finds the test statistic, tail probability, critical value, and decision.

Meaning of the P Value

The p value measures the probability of seeing a z score at least as extreme as the observed result, assuming the null hypothesis is true. For a right tailed test, the tool uses the area to the right of z. For a left tailed test, it uses the area to the left.

Input Choices

You can work from a known z score, a sample mean, or a sample proportion. The z score option is fastest when another source already gave the statistic. The mean option is useful for quality control, exam averages, weights, and process measurements. The proportion option helps with rates, percentages, conversion counts, and survey shares.

Alpha and Decision

Alpha is your chosen risk level. Common choices are 0.10, 0.05, and 0.01. If the p value is less than or equal to alpha, the result is statistically significant. The calculator also prints the one sided critical z score. This helps you compare the statistic with the rejection boundary.

Direction Matters

The direction matters before results are inspected. A right tailed test supports a claim such as greater than, higher than, or increased. A left tailed test supports lower than, reduced, or less than. Changing direction after seeing data can make the conclusion misleading.

Reporting

This page is designed for transparent checking. It reports inputs, standard error, z statistic, p value, and conclusion. Exports help you save a record for homework, reports, lab notes, or audit files.

Assumptions

Use clean data and match the test to your design. Independent observations are important. For means, use the known population standard deviation. For proportions, keep expected successes and failures large enough. When assumptions are weak, consider a t test, exact binomial test, or another model. Because statistical results guide choices, avoid treating significance as practical importance. A tiny effect can be significant in a huge sample. A useful report should include the context, sample size, direction, alpha, p value, and a plain sentence explaining the decision. This makes the result easier to review later.

FAQs

What is a one tailed z test?

It is a hypothesis test that checks evidence in one direction only. The alternative claim is either greater than or less than the null value.

When should I use a right tailed test?

Use it when the alternative claim says the true mean, proportion, or score is greater than the null value.

When should I use a left tailed test?

Use it when the alternative claim says the true value is lower than the null value. The p value uses the left normal tail.

What does alpha mean?

Alpha is the chosen significance level. It is the cutoff risk for rejecting a true null hypothesis. Common values are 0.05 and 0.01.

What does a small p value show?

A small p value shows that the observed result is unlikely under the null hypothesis. If it is at or below alpha, reject the null.

Can I use this for a sample mean?

Yes. Use the mean mode when you know the sample mean, hypothesized mean, population standard deviation, and sample size.

Can I use this for a proportion?

Yes. Use the proportion mode when your data has successes, total sample size, and a hypothesized population proportion.

Does this replace statistical judgment?

No. The calculator checks formulas and decisions. You still need correct assumptions, clean data, and a suitable test design.