One Sample t test and One Sample Test for Variance.
At the beginning of the course of Statistical Methods I, the instructor recommended that students devote 3 hours per week for the duration of the 13-week semester, for a total of 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 10 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:
|
45
|
38
|
37
|
40
|
44
|
|
38
|
46
|
37
|
42
|
43
|
a. work out the sample mean and sample standard deviation.
b. Formulate a suitable null and alternative hypothesis to test the students' claim that they followed their instructor's recommendation at a 5 level of significance and interpret your findings.
c. Estimate and interpret the p-value of the calculated test statistic in (a) above.
d. If the same sample results had been obtained from a random sample of 16 students, could the students' claim be accepted at a lower level of significance than in part (c)?
e. whilst dealing with 16 students, suppose that the alternative hypothesis has been one-sided and that it was set as Ha: m < 39. Make a graph to visualize the problem and state, without doing the calculations, whether the p-value of the test (the level of significance needed to reject the null hypothesis) would be higher than, lower than, or the same as found in (d).
f. Using the original data, test at the 5 percent significance level that the population standard deviation of studying times is greater than 4 hours.
g. Using original data, estimate the population standard deviation with 90% probability.