How to find p value given z and alpha?

The p value is a statistical measure that helps determine the strength of evidence against the null hypothesis in hypothesis testing. When conducting statistical tests, we often rely on the z-score to calculate the p value. In this article, we will discuss how to find the p value given z and alpha, along with 12 related FAQs.

How to Find p Value Given z and Alpha?

To find the p value given z and alpha, follow these steps:

Step 1: Determine the level of significance (alpha value) for your statistical test. This is usually predetermined based on the specific research study or experiment.

Step 2: Identify the critical value associated with the alpha value. The critical value, denoted as zα, represents the z-score which corresponds to the alpha value in the standard normal distribution table.

Step 3: Calculate the z-score of the test statistic. The test statistic depends on the specific hypothesis test you are conducting. For example, if you are conducting a z-test for a population mean, you would calculate the z-score using the sample mean, population mean, and standard deviation.

Step 4: Compare the calculated z-score with the critical value (zα). If the calculated z-score falls within the critical region (on the tails of the distribution), then the p value will be less than the alpha value. Conversely, if the calculated z-score does not fall within the critical region, the p value will be greater than the alpha value.

Step 5: Determine the p value. Based on the comparison made in the previous step, you can find the p value by subtracting the cumulative probability of the standardized normal distribution from the value of 1. This will give you the p value corresponding to your z-score.

Example: Let’s say you are conducting a hypothesis test on the average height of students. You choose a significance level of 0.05 (alpha = 0.05). The critical value associated with this alpha value is z0.05 = 1.645. If your calculated z-score is 2.34, which falls into the critical region, you can find the p value by subtracting the cumulative probability from 1. In this case, the p value would be 1 – P(Z ≤ 2.34).

It is essential to find the p value given z and alpha to make informed decisions in statistical hypothesis testing. By comparing the observed test statistic (z-score) with the critical value, you can determine whether the results are statistically significant (reject the null hypothesis) or not (fail to reject the null hypothesis). The p value further quantifies this significance level by providing the probability of obtaining the observed test statistic or a more extreme value if the null hypothesis is true.

Related FAQs:

1. What is the p value?

The p value is a statistical measure that quantifies the evidence against the null hypothesis in hypothesis testing.

2. What is the null hypothesis?

The null hypothesis is a statement of no effect or no difference that is tested in statistical hypothesis testing.

3. What is the alpha value?

The alpha value, also known as the significance level, represents the probability of rejecting the null hypothesis when it is true.

4. What is the critical value?

The critical value is a specific value associated with an alpha level that helps determine the cutoff point for rejecting or failing to reject the null hypothesis.

5. What is a z-score?

A z-score is a standardized value that represents the number of standard deviations an observation or test statistic falls from the mean of a distribution.

6. What is a z-test?

A z-test is a statistical test used to compare a sample mean to a known population mean, assuming that the population standard deviation is known.

7. What is the cumulative probability?

The cumulative probability refers to the probability of observing a value less than or equal to a specific point on a distribution.

8. What does it mean if the p value is less than the alpha value?

If the p value is less than the alpha value, it suggests that the observed test statistic is statistically significant, and we can reject the null hypothesis.

9. What does it mean if the p value is greater than the alpha value?

If the p value is greater than the alpha value, it indicates that the observed test statistic is not statistically significant, and we fail to reject the null hypothesis.

10. How can I find the cumulative probability using a z-table?

By locating the z-score in the z-table and identifying the corresponding cumulative probability, you can determine the cumulative probability.

11. Can I find the p value if I know the test statistic but not the z-score?

Yes, you can find the p value using the test statistic if it follows a known distribution other than the standard normal distribution.

12. Can I directly compare p values from different hypothesis tests?

No, p values obtained from different hypothesis tests should not be directly compared, as they are specific to each particular test and its assumptions.

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