At the beginning of the course of Statistical Methods I, the instructor recommended that students devote at least 3 hours per week for the duration of the 13-week semester, for a total of at least 39 hours. It is known that the times spent on studying statistics follow a normal distribution. Throughout the courses duration, students were claiming that they were following the instructors recommendation. At the courses completion, a random sample of 9 students enrolled in the course was drawn where each student was asked how many hours he or she spent doing homework in statistics.

The data are listed below:

42 36 35 38 41 36 41 36 40

a) Calculate the sample mean and sample standard deviation.

b)Formulate a suitable null and alternative hypothesis to support the students claim that they followed their instructors recommendation at a 5% level of significance.

ii. What is the decision rule for this test?

iii. Calculate the test statistic.iv.

iv. What is your conclusion regarding the students average study time?

4c) If the sample results had been obtained from a random sample of 16 students,would the conclusion about the students claim be different from in part (b)? Explain

d) Using the original data, test at the 5% significance level whether the population standard deviation of studying times is greater than 3 hours.

PLEASE SHOW ALL YOUR WORK.