The Federal Drug Administration wishes to determine whether the claims that Vitamin C prevents colds has any truth. In a clinical drug trial, 30 subjects were randomly assigned to either the Vitamin C group (receiving a daily supplement of the minimum daily requirement) or the placebo group (who received no supplement but did get a placebo pill). The number of self- reported colds is recorded after three years. Number of colds in 3 years: Vitamin C group: 3, 8, 6, 7, 4, 9, 2, 5, 7, 11, 10, 8, 7, 6, 7 Placebo group: 8, 8, 7, 10, 11, 4, 3, 7, 6, 8, 4, 10, 6, 8,5 The value of the numerator (either + or -) in the t test formula for Problem 3 is _____. Then what is the degrees of freedom and what is the derived t value ? Also, what can be concluded from the statistical analysis and what significance level should be reported?
(I want to compare my answers to yours, because I have different answers than what was given to me earlier on this site, and I don;t understand why...thank you.)
H0: Null Hypothesis: ( Vitamin C does not prevent colds )
HA: Alternative Hypothesis: ( Vitamin C prevents colds ) (claim)
From the given data, the following statistics are calculated:
n1 = 15
1 = 6.6667
s1 = 2.4689
n2 = 15
2 = 7
s2 = 2.3604
Pooled standard deviation (sP) is given by:
Test Statistic is given by:
t = (6.6667-7.0)/0.8819
= - 0.3333/0.8819
= - 0.3779
ndf = n1 + n2 - 2 = 15 + 15 - 2 = 28
Take = 0.05
One Tail - left side test
From Table, critical value of t = - 1.7011
Since calculated value of t = - 0.3779 is greater than critical value of t = - 1.7011, the difference is not significant. Fail to reject null hypothesis.
The data do not support the claim that Vitamin C prevents colds.
Answers to Questions asked:
(a) The value of the numerator (either + or -) in the t test formula for Problem 3 = - 0.3333
(b) the degrees of freedom = 28
(c) the derived t value = - 1.7011
(d) Conclusion: The difference is not significant. Fail to reject null hypothesis. The data do not support the claim that Vitamin C prevents colds.
(e) significance level = 0.05