A one-tail test for the population mean μ produces a test-statistic z = −0.75.The p-value associated with the test is 0.7734.

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The p-value for a z-score of -0.75 in a one-tail test is approximately 0.2266, not 0.7734. The p-value represents the probability of obtaining a test statistic at least as extreme as the one observed, under the assumption that the null hypothesis is true. For negative z-scores in a one-tail test, the p-value is found by looking up the z-score in a standard normal distribution table or using a calculator, which gives the area to the left of the z-score.

A One-Tail Test for the Population Mean μ Produces a Test-Statistic