A statistician performs the test versus and finds the p-value to be .4546.
a. The statistician performing the test does not tell you the value of the sample mean and the value of the test statistic. Despite this, you have enough information to determine the pair of p-values associated with the following alternative hypotheses.
i. H1: µ < 15
ii. H1: µ > 15
You will need more information to determine which p-value goes with which alternative. Determine the pair of p-values. Here the value of the sample mean is the same in both cases.
b. Suppose the statistician tells you that the value of the test statistic is negative. Match the p-values with the alternative hypotheses. The result for one of the two alternatives implies that the sample mean is not on the same side of µ = 15 as the rejection region. Although we have not discussed this scenario in the book, it is important to recognize that there are many real-world scenarios in which this type of situation does occur. For example, suppose the EPA is to test whether or not a company is exceeding a specific pollution level. If the average discharge level obtained from the sample falls below the threshold (mentioned in the null hypothesis), then there would be no need to perform the hypothesis test.