Calculate sample mean and sample standard deviation for the given set of data. Formulate null and alternative hypothesis to test the claim that the sleeping pill is effective at a 1 percent level of significance.
A pharmaceutical company wants to test the effectiveness of an experimental sleeping pill. An experiment is conducted over two nights, with 10 volunteers who have difficulties sleeping at night. On the first night, each of the ten persons is given the sleeping pill one hour before bedtime and the time needed to fall asleep is recorded. On the second night, the same persons are given a placebo in the form of a pill that looks exactly as the real one (without being told about it) and the time needed to fall asleep is again recorded. The times needed to fall asleep are assumed to follow a normal distribution. The results for the two nights for the ten volunteers are shown below:
|
Individual
|
A
|
B
|
C
|
D
|
E
|
F
|
G
|
H
|
I
|
J
|
|
Pill
|
4
|
7
|
10
|
15
|
6
|
13
|
6
|
11
|
1
|
11
|
|
Placebo
|
7
|
8
|
9
|
16
|
10
|
15
|
8
|
15
|
4
|
10
|
Compute the mean and variance of the sample data.