Question

A new vaccination is being used in a laboratory experiment to investigate whether it is effective. There are 203 subjects in the study. Is there sufficient evidence to determine if vaccination and disease status are related?

Vaccination Status	Diseased	Not Diseased	Total
Vaccinated	42	37	79
Not Vaccinated	58	66	124
Total	100	103	203

Copy Data

Step 4 of 8:

Find the value of the test statistic. Round your answer to three decimal places.

Answer 1

Solution:

Test statistic formula is given as below:

Chi square = ∑[(O – E)^2/E]

Where, O is observed frequencies and E is expected frequencies.

E = row total * column total / Grand total

Calculation tables for test statistic are given as below:

Observed Frequencies
	Column variable
Row variable	Diseased	Not Diseased	Total
Vaccinated	42	37	79
Not Vaccinated	58	66	124
Total	100	103	203

Expected Frequencies
	Column variable
Row variable	Diseased	Not Diseased	Total
Vaccinated	38.91626	40.08374	79
Not Vaccinated	61.08374	62.91626	124
Total	100	103	203

Calculations
(O - E)
3.083744	-3.08374
-3.08374	3.083744

(O - E)^2/E
0.244357	0.23724
0.155679	0.151145

Test Statistic = Chi square = ∑[(O – E)^2/E] = 0.788422

χ² test statistic = 0.788