Question

Twenty volunteers at a cold research institute caught a cold after having been exposed to various cold viruses. Ten of the volunteers were randomly selected to receive tablets containing 1 gram of vitamin C. These tablets were taken four times a day. The control group, consisting of the other 10 volunteers, was given placebo tablets that looked and tasted exactly like the vitamin C ones. This was continued for each volunteer until a doctor, who did not know whether one volunteer was receiving vitamin C or the placebo, decided that the volunteer was no longer suffering from the cold. The length of time the cold lasted was then recorded. At the end of the experiment, the following data resulted:

Treated With Vitamin C	Treated With Placebo
5.5	6.5
6.0	6.0
7.0	8.5
6.0	7.0
7.5	6.5
7.5	7.5
5.5	6.5
7.0	7.5
6.5	6.0
6.0	8.0

1. there sufficient evidence to conclude that the mean time for patients treated with vitamin C is less than the mean time for the patients treated with placebo? Use a=.01.

Answer 1

using excel

t-test

t-Test: Two-Sample Assuming Equal Variances
	treated With Vitamin C	Treated With Placebo
Mean	6.45	7
Variance	0.580555556	0.722222222
Observations	10	10
Pooled Variance	0.651388889
Hypothesized Mean Difference	0
df	18
t Stat	-1.523798419
P(T<=t) one-tail	0.072467779
t Critical one-tail	2.55237963
P(T<=t) two-tail	0.144935558
t Critical two-tail	2.878440473

this is left-tailed test

p-value = 0.07246 > 0.01( alpha)

we fail to reject the null hypothesis

there is not sufficient evidence to conclude that the mean time for patients treated with vitamin C is less than the mean time for the patients treated with placebo