Question

Of the 94 participants in a drug trial who were given a new experimental treatment for arthritis, 57 showed improvement. Of the 89 participants given a placebo, 51 showed improvement. 0.05 Significance

1) Assuming independence between the two variables, find the expected frequency for each cell of the table.

Table of expected frequencies:

Improvement. No improvement

Drug ____________. _______________

Placebo__________. _______________

2) Find the value of the x2 test statistic

X2= _____

3) use the given significance level to find the x2 critical value.

The critical value is ____

Answer 1

Following is 2 by 2 table shows the given data:

	Improvement	No improvement	Total
Drug	57	94-57=37	94
Placebo	51	89-51=38	89
Total	108	75	183

Expected frequencies will be calculated as follows:

Following table shows the expected frequencies:

	Improvement	No improvement
Drug	55.475	38.525
Placebo	52.525	36.475

Following table shows the calculations for chi square test statistics:

O	E	(O-E)^2/E
57	55.475	0.04192204
51	52.525	0.04427653
37	38.525	0.06036665
38	36.475	0.06375942
Total		0.21032464

Following is the test statistics:

3)

Degree of freedom: df =( number of rows -1)*(number of columns-1) = (2-1)*(2-1)=1

The critical value for 0.05 significance level is 3.841

Since test statistics is less than 3.841 so we fail to reject the null hypothesis.