A pharmaceuticals company claims to have developed a cure for the common cold. I
ID: 3393928 • Letter: A
Question
A pharmaceuticals company claims to have developed a cure for the common cold. In order to test whether this is true, one group of recent cold-sufferers was given this medicine and another group was given a placebo instead. The selection process was completely random.
The participants were examined two hours after they were given the medicine or placebo. The results are tabulated below:
You plan to test whether the medicine has any effect on the cold by conducting a chi-square test for association on the data available. Calculate the chi-square test statistic (2) using SPSS. Give your answer to 4 decimal places.
a)2 =
b)At = 0.05, the null hypothesis that the medicine has no effect is (rejected or not rejected).
Placebo Medicine Total No Effect 33 43 76 Cold Cured 25 32 57 Total 58 75 133Explanation / Answer
a)
Doing an Expected Value Chart,
33.14285714 42.85714286
24.85714286 32.14285714
Using chi^2 = Sum[(O - E)^2/E],
chi^2 = 0.002547893 [ANSWER]
******************************
b)
With df = (a - 1)(b - 1), where a and b are the number of categories of each variable,
a = 2
b = 2
df = 1
Thus, the critical value is
significance level = 0.05
chi^2(critical) = 3.841458821
As chi^2 < 3.8414, we the null hypothesis that the medicine has no effect is NOT REJECTED. [ANSWER]
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