Question

A hypothetical study examined the effectiveness of a new sleep aid. A random sample of volunteers recorded the number of hours they slept after taking a placebo. On the next night the same volunteers recorded the number of hours they slept after taking the new drug. The data are summarized below. The differences were normally distributed.

Volunteer	Hours of sleep after drug	Hours of sleep after placebo	Difference
1	10.1	5.2	4.9
2	6	8.3	-2.3
3	8.2	3.9	4.3
4	8	4.7	3.3
5	6.5	5.3	1.2
6	5.4	7.4	-2
7	6.9	4.2	2.7
8	6.7	6.1	0.6
9	8.2	4.8	3.4
10	5.8	7.3	-1.5
average	7.18	5.72	1.46
standard deviation	1.43	1.49	2.67

a) What is the null hypothesis for this study?

b) What statistical test should be used to test the null hypothesis?

c) What is the test statistic associated with these data?

d) What df are associated with these data?

e) Is the P-value “significant” at alpha=0.05? Write "yes" or "no".

Answer 1