Question

Exercise 3. The data set in the file “NightSleepData.xlxs” contains the number of hours of night sleep for a random sample of students.

(a) Construct a 95% CI for the true mean number of hours of night sleep. (b) Conduct the test of whether the mean number of hours of night sleep exceeds 6.5 hours.

10	7	6.5	8	7	8
4	5	7	5	5	5.5
5.5	8	6.5	5	7	7
5.5	7	6	5	8.5	8
7	7.5	6	9	10	8
6	9	6.5	5	9	5
5.5	7	8	8	6	6.5
5.5	5	5	10.5	7	5
7.5	7	8.5	5	6	9.5
4.5	7	6.5	9	10	6

Answer 1

a.

Sample mean:

Sample standard deviation:

95% CI for the true mean number of hours of night sleep:

b.

Hypothesis:

Test statistic,

Degrees of freedom = n-1 = 60 - 1 = 59

Critical value = 1.671

Since calculated value of test statistic is less than critical value we accept null hypothesis at 5% level of significance and conclude that the mean number of hours of night sleep does not exceeds 6.5 hours.