Question

A new vaccination is being used in a laboratory experiment to investigate whether it is effective. There are 242 subjects in the study. Is there sufficient evidence to determine if vaccination and disease status are related?

Vaccination Status	Diseased	Not Diseased	Total
Vaccinated	48	91	139
Not Vaccinated	62	41	103
Total	110	132	242

H0: vaccination and disease status are independent

Ha: vaccination and disease status are dependent

E(n1,1)=63.2 E(n1,2)=75.8

Test Statistic=15.752

Degrees of freedom=1

Step 6 of 8: Find the critical value of the test at the 0.05 level of significance. Round your answer to three decimal places.

Step 7 of 8: Make the decision to reject or fail to reject the null hypothesis at the 0.05 level of significance.

Step 8 of 8: State the conclusion of the hypothesis test at the 0.05 level of significance.

Answer 1

(32 Solution Given Not Diseased Total Vaccination status Diseased 139 Vaccinated 48 103 41 Not Vaccinated 242 I lo - Total Now to state the null and alternative hypothesis :- independent. licence Stores are Null hypothesis Ho: Vaccination and disease status are " Alterative hypothesis Hei Vaccination and disease Now to find the expected values of each cell - Row total x Column total Expected Value - Grand total Vaccination status Diseased Not diseased Total Vaccinated 139X132 139 disease status are dependent. Hothesis Ha: Vaccination and 139 Xiro 949 -63.18 942 = 75.89 103 X132 Vot vaccinated 103 X 110 1242 =4 6-82 103 242 = 56.18 Total llo 139 242 wow to find the test -statistic, is We know that The formula x? test stabilic is given by

10) x?- (48-6348)2 (91-75-82) 2 (62-46.82)2 (41-56.18)2 63.18 + - 75.82 ' 46.82 T 56.18 = 3.6472+ 3.0392+ 4.9217+ 4.1017 [x² 15.7098 Now df = (r-) ((-1) = (2-1) (2-1) = 0 (0) IdF = 1 Step 6 Now to find the coitial value x critical =X²2, df 10.85) = 3.8414 Therefore the critical value of the test at the 0.05 level of significance is 3-84 1 Step 1 Decision X Britical <x statistic 3-841 <15.7098 so we reject the null hypothesis (Ho) at 0.05 level of significance sve onclusion: There is sufficient evidence to reject the Ho at 0.05 level of significance.