Problem 15BSC
In Exercise, test the given claim.
Clinical Trial of Echinacea In a clinical trial of the effectiveness of echinacea for preventing colds, the results in the table below were obtained (based on data from “An Evaluation of Echinacea Angustifolia in Experimental Rhinovirus Infections,” by Turner et al., New England Journal of Medicine, Vol. 353, No. 4). Use a 0.05 significance level to test the claim that getting a cold is independent of the treatment group. What do the results suggest about the effectiveness of echinacea as a prevention against colds?

Treatment Group 


Placebo 
Echinacea: 20% extract 
Echinacea: 60% extract 
Got a Cold 
88 
48 
42 
Did Not Get a Cold 
15 
4 
10 
Answer:
Step 1 of 2

Treatment Group 


Placebo 
Echinacea: 20% extract 
Echinacea: 60% extract 
Total 
Got a Cold 
88 
48 
42 
178 
Did Not Get a Cold 
15 
4 
10 
29 
Total 
103 
52 
52 
207 
The solution to this problem takes four steps: (1) state the hypotheses, (2) formulate an analysis plan, (3) analyze sample data, and (4) interpret results. We work through those steps below:
State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.
H0: The claim that the amount of smoking is independent of seat belt use
H1: The claim that the amount of smoking is not independent of seat belt use
Formulate an analysis plan. For this analysis, the significance level is 0.05. Using sample data, we will conduct a chisquare test for independence.
Applying the chisquare test for independence to sample data, we compute the degrees of freedom, the expected frequency counts, and the chisquare test statistic.
DF = (r  1) (c  1) = (2  1) (3  1) = 2

Treatment Group 


Placebo 
Echinacea: 20% extract 
Echinacea: 60% extract 
Total 
Got a Cold 
88 
48 
42 
178 
Did Not Get a Cold 
15 
4 
10 
29 
Total 
103 
52 
52 
207 
= 88.57
= 44.7149
= 44.7149
= 14.4299
= 7.285
= 7.285
SL. No. 
O 
E 
(O  E )2 
(O  E)2/E 
1 
88 
88.57 
0.3249 
0.003668 
2 
48 
44.7149 
10.79188 
0.241349 
3 
42 
44.7149 
7.370682 
0.164837 
4 
15 
14.4299 
0.325014 
0.022524 