# Question

Using the information in Table 5.8, answer the following questions.

In table

a. If the population has a normal distribution, then the population mean and median are identical. Thus, either the mean or the median could be used to represent the center of the population. In this situation, why is the t test more appropriate than the sign test for testing hypotheses about the center of the distribution?

b. Suppose the population has a distribution that is highly skewed to the right. The researcher uses an α = .05 t test to test hypotheses about the population mean. If the sample size is n = 10, will the probability of a Type I error for the test be .05? Justify your answer.

c. When testing hypotheses about the mean or median of a highly skewed population, the difference in power between the sign and t tests decreases as the size of (Ma – M0) increases. Verify this statement using the values in Table 5.8. Why do think this occurs?

d. When testing hypotheses about the mean or median of a lightly skewed population, the difference in power between the sign and t tests is much less than that for a highly skewed population distribution. Verify this statement using the values in Table 5.8. Why do you think this occurs?

In table

a. If the population has a normal distribution, then the population mean and median are identical. Thus, either the mean or the median could be used to represent the center of the population. In this situation, why is the t test more appropriate than the sign test for testing hypotheses about the center of the distribution?

b. Suppose the population has a distribution that is highly skewed to the right. The researcher uses an α = .05 t test to test hypotheses about the population mean. If the sample size is n = 10, will the probability of a Type I error for the test be .05? Justify your answer.

c. When testing hypotheses about the mean or median of a highly skewed population, the difference in power between the sign and t tests decreases as the size of (Ma – M0) increases. Verify this statement using the values in Table 5.8. Why do think this occurs?

d. When testing hypotheses about the mean or median of a lightly skewed population, the difference in power between the sign and t tests is much less than that for a highly skewed population distribution. Verify this statement using the values in Table 5.8. Why do you think this occurs?

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