Question

Eight students in a statistics class were asked to report the number of hours they slept on weeknights and on weekends. The table shows the results.

Student #             1 2 3 4 5 6 7 8

weeknight hours   8 5.5 7.5 8 7 6 6 8

weekend hours     4 7 10.5 12 11 9 6 9
a) How can you tell that this is a problem involving dependent samples?  
b) Create a 90% confidence interval on the mean difference and interpret the intervals in the context of the problem.    
c) Write the two hypotheses for the problem.   
d) Perform a statistical test on the difference in the number of hours slept on weeknights vs. weekend nights and report your test statistic and p-value. Sketch the distribution of test statistics and indicate your test statistic as well as the shaded region corresponding to p.   
e) Make a conclusion based on your test.

Answer 1

a) Yes, this is dependent samples since students are same for both samples

b) From the samples

Weeknight	Weekend	Difference (d)
8	4	4
5.5	7	-1.5
7.5	10.5	-3
8	12	-4
7	11	-4
6	9	-3
6	6	0
8	9	-1

c) H0: There is no significance difference among the mean hours they slept on weeknights and on weekends.

H1:  There is significance difference among the mean hours they slept on weeknights and on weekends.

Let the los be alpha = 10%

d)

Test Statistic t = -1.563 / (2.665/sqrt(8) ) = -1.6583

Critical t: ±1.8946
P-Value: 0.1412

Here t value is in t critical value and P-value > alpha 0.05 so we accept H0

e) Thus we conclude that there is no significance difference among the mean hours they slept on weeknights and on weekends.