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?

11 10 (Ma-Mal ur Populatiorn Distributio Statistic Lvl 2 6 Level .268Level 2 8 t05 145 543 754 05 182 14 903 0 217 827 964 Sign .055.136 .454.642 .059 .172 .604 104.058 194 .704.889 Heavily Tailed03 104 3 510 049 15 46 .648 045 163 554 736 Sign 055 209 715 869 059 278 866 964 058 325 935 990 Lightly Skewed 055140 454 631 059 178 604 .794 058 201 .704 881 Sign 025.079 .437.672 .037 .129 .614864041 .159 .762935 Highly Skewed007 055 277 463 006 078 515 733 0104 658 873 Sign 055 196 613 778 059 258 777 912 058 301 867 964 Normal