This P-Value from Z Score Calculator helps you find left-tailed, right-tailed, and two-tailed p-values from a given z-test statistic. It provides instant results along with a clear, step-by-step explanation showing you how to find these p-values using a standard normal (Z) table. Simply enter your z-score to calculate accurate p-values up to six decimal places.
Free P-Value From Z Score Calculator
Want to use the critical value approach instead? Use the z critical value calculator.
What is a P-Value in a Z-Test?
A p-value in a z-test is the probability of obtaining a sample result at least as extreme as the observed z-statistic, assuming the null hypothesis is true. It is useful when you want to make decisions on whether to reject or fail to reject the null hypothesis in a z-test (either for the sample mean(s) or sample proportion(s)).
The decision is to reject the null hypothesis if the p-value is less than a pre-defined significance level (α). Otherwise, you fail to reject the null hypothesis.
How to Find P-Values for a Z-Test Using the Calculator
Are you working on z-test questions for an exam or homework, and need a quick way to find p-values for these tests? You only need the p-value from the Z calculator. Here’s how you can find p-values for a right-tailed, left-tailed, and two-tailed z-tests using this calculator:
- Step 1. Enter your Z-score in the input box (A z-test statistic can either be negative or positive. You should enter the number as it is)
- Click the “Calculate P-Values” button.
The calculator will instantly return the left-tailed p-value, right-tailed p-value, and two-tailed p-value for your z-test. Therefore, your work will be just to select the right p-value for your test. The calculator will also show you how to find these p-values using z-tables, step-by-step.
Examples: Finding P-values From Z Using the Calculator
To help you learn how you can leverage this tool to quickly find the correct p-value for your test, follow these examples:
Example 1: Left-Tailed Test
Scenario: You conduct a one-sample z-test to check if the proportion of students passing an exam is less than 70%. The test statistic is z = -1.50. Find the appropriate p-value for this test.
Solution
Here, we need to test the hypotheses:
H0: p = 0.70
H1: p < 0.70
This is a left-tailed test. Thus, we need to find the left-tailed p-value.
Using the Calculator:
- Enter -1.50 in the z-score input field
- Click the “Calculate p-values” button
- Select the left-tailed p-value.
The calculator shows that the correct p-value for this test is 0.066807, as shown below.
Therefore, if you’re testing the hypothesis at 5% significance level, then you should fail to reject the null hypothesis since the p-value (0.0668) is greater than 0.05 significance level.
The conclusion would be: there is no sufficient evidence to conclude that the proportion of students passing an exam is less than 70%.
Example 2: Right-Tailed Test
Scenario: A company claims its new battery lasts at least 100 hours. You collect sample data and calculate a z-test statistic = 2.33 to check if the battery lasts more than 100 hours. Find the appropriate p-value for this test.
Solution
In this case, we need to test the hypotheses:
H0: ÎĽ = 100 hours
H1: ÎĽ > 100 hours
This is a right-tailed test (ÎĽ > 100). As such, we need to calculate the right-sided p-value for the test.
Using the Calculator:
- Enter 2.33 in the z-score input field
- Click the “Calculate P-values” button
- Select the right-tailed p-value
The calculator returns the right-tailed p-value for the test as 0.009900, as shown below.
If you’re testing the hypothesis at a 0.05 significance level, you would reject the null hypothesis since the p-value (0.0099) is less than the 0.05 significance level.
The conclusion would be: there is sufficient evidence to support the claim that the new battery lasts more than 100 hours.
Example 3: Two-Tailed Test
Scenario: A researcher wants to test if a new teaching method changes the average score of students. The population average is known to be 75, and the researcher found the z-test statistic = 2.67. Find the correct p-value for this test.
Solution
Here, the hypotheses are:
H0: ÎĽ = 75
H1: μ ≠75
This is a two-tailed test (≠), also known as a non-directional test. To find the correct p-value using the calculator, follow these steps:
- Enter 2.67 in the z-score input field
- Click the “Calculate P-values” button
- Select the Two-tailed P-value
The calculator returns the two-tailed p-value for the test as 0.007585, as shown below.
Suppose the researcher wanted to test the hypothesis at 1% level, then we should reject the null hypothesis since the p-value (0.0076) is less than the 0.01 significance level.
The conclusion would be: there is sufficient evidence to conclude that the new teaching method changes the average score of students.
Frequently Asked Questions
A p-value to Z-Score calculator is an online tool that lets you quickly find the p-value for any z-test. The calculator returns left-tailed, right-tailed, and two-tailed p-values for your test with a click of a button.
Simply enter your Z test statistic value into the input box and click Calculate P-Values. The calculator will instantly display the left-tailed, right-tailed, and two-tailed p-values. It will also show you how to find these p-values using a standard normal table, step-by-step.
Yes! Negative Z test statistic values are valid and occur when your sample statistic is below the population mean. The calculator correctly handles negative Z-scores for all test types.
No. A p-value is a probability, so it always ranges from 0 to 1. Our calculator ensures correct calculations for left-tailed, right-tailed, and two-tailed tests. Therefore, you will never see a value greater than 1.
Not necessarily. The calculator gives instant results. However, it also explains how to find p-values manually using Z-tables. This is helpful for learning or verifying calculations for exams and assignments.