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:

	Placebo	Medicine	Total
No Effect	36	49	85
Cold Cured	39	38	77
Total	75	87	162

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 (χ²) using SPSS. Give your answer to 4 decimal places.

a) χ² =

b)At α = 0.05, the null hypothesis that the medicine has no effect is (rejected / not rejected)

Answer 1

a) The observed and expected values are as below

Observed
	Yes	No	Total
Men	36	49	85
Women	39	38	77
Total	75	87	162
Expected
	Yes	No	Total
Men	39.35	45.65	85
Women	35.65	41.35	77
Total	75	87	162

Chi square is calculated as below.

Number	Observed	Expected	(O-E)	(O-E)2	(O-E)2/E
1	36	39.35	-3.35	11.23491084	0.2855
2	39	35.65	3.35	11.23491084	0.3152
3	49	45.65	3.35	11.23491084	0.2461
4	38	41.35	-3.35	11.23491084	0.2717
Total					1.1185

Chi Square = 1.1185

(b) The p value for chi square = 1.1185 is 0.2900

Since op value is > Alpha, the null hypothesis that the medicine has no effect is not rejected,