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 course?s duration, students were claiming that they were following the instructor?s recommendation. At the course?s 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 instructor?s recommendation at a 5% level of significance.
Mean
Standard Error
Standard
Deviation

38.3333
3
0.89752
7
2.69258
2

Ho: U &lt;= 39
H1: U &gt; 39
Reject null hypothesis when p &gt; 0.05

T test statistic = (sample mean ? mu)/SE
=(38.33-39)/…