Question

A new vaccination is being used in a laboratory experiment to investigate whether it is effective. There are 252252 subjects in the study. Is there sufficient evidence to determine if vaccination and disease status are related?

Vaccination Status   Diseased   Not Diseased   Total
Vaccinated 54 55   109
Not Vaccinated 71 72   143
Total 125 127   252

State the null and alternative hypothesis.

Find the expected value for the number of subjects who are vaccinated and are diseased. Round your answer to one decimal place.

Find the expected value for the number of subjects who are vaccinated and are not diseased. Round your answer to one decimal place.

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

Find the degrees of freedom associated with the test statistic for this problem.

Find the critical value of the test at the 0.01 level of significance. Round your answer to three decimal places.

Make the decision to reject or fail to reject the null hypothesis at the 0.01 level of significance

State the conclusion of the hypothesis test at the 0.01 level of significance.

Answer 1

Observed Values: C1 R1 54 R2 71 Column Total 125 C2 55 72 127 Row Total 109 143 252 Expected Values = [(Row total x Column total)/Grand total] C1 C2 R1 54.0675 54.9325 R2 70.9325 72.0675

0 E (0-E)?/E 54 54.0675 0.0001 71 70.9325 0.0001 55 54.9325 0.0001 72 72.06750.0001 Total 0.0003 7 = (0-5) = 0.0003 E Number of rows =r= 2 Number of columns =C = 2 D.F =(r-1)x(C-1) = 1 Significance level= a = 0.01

Critical value = 6.635 [using Excel function CHIINV(0.01,1)] Decision rule : Reject H0 if x² > 6.635 Here x²=0 < 6.635 Conclusion: By decision rule, we fail to reject HO

Answers:

State the null and alternative hypothesis.

H0 : vaccination and disease status are independent.

H1 : vaccination and disease status are related

Find the expected value for the number of subjects who are vaccinated and are diseased.

Ans : 54.1

Find the expected value for the number of subjects who are vaccinated and are not diseased.

Ans : 54.9

Find the value of the test statistic.

Ans : 0.000

Find the degrees of freedom associated with the test statistic for this problem.

Ans : 1

Find the critical value of the test at the 0.01 level of significance.

Ans : 6.635

Make the decision to reject or fail to reject the null hypothesis at the 0.01 level of significance

Ans :  fail to reject the null hypothesis

State the conclusion of the hypothesis test at the 0.01 level of significance.

Ans : There is insufficient evidence to conclude that vaccination and disease status are related.