A pharmaceuticals company claims to have developed a cure fo

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).

Solution

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]

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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]