In a test of the hypothesis Ho: µ = 50 vs. Ha: µ ≠ 50, a sample of n = 100 observations possessed the mean, sample mean (x-bar) of 50.3 and a standard deviation s = 2.1. Find the p-value for this test.

Solution: We need to test

This corresponds to a two-tailed test. The z-statistics is computed as

The p-value is defined as

Since the p-value is not less than the significance level (0.05), we fail to reject the null hypothesis.