Question

In a test of $H_0:\mu =100$against$H_a:\mu >100$, the sample data yielded the test statistic z = 2.17. Find and interpret the p-value for the test.

Short answer

The p-value is 0.0150, representing the probability of the test statistic being more than 2.17 when the claim $\mu =100$is true.

Step-by-step solution

Given information

The hypothesis test is: $H_0:\mu =100$versus $H_a:\mu >100$.

The test statistic is z = 2.17.

Computing the p-value

The p-value for the one-tailed test is:

$$\begin{gathered} p=P\left(Z>2.17\right) \\ =1-P\left(Z⩽2.17\right) \\ =1-0.9850 \\ =0.0150 \end{gathered}$$

The probability of a z-score less than or equal to 2.17 is obtained from the z-table.

Therefore, the p-value is 0.0150.

Interpretation of the p-value

The p-value represents the probability of the test statistic being more than 2.17 when the claim $\mu =100$is true.