Question

A new vaccination is being used in a laboratory experiment to investigate whether it is effective. There are 271 subjects in the study. Is there sufficient evidence to determine if vaccination and disease status are related? Naccination Status Diseased Not Diseased Total Vaccinated 59 53 112 Not Vaccinated 76 83 159 Total 135 136 271 Copy Data Step 1 of 8: State the null and alternative hypothesis. Answer 2 Points Tables Keypad Ho: vaccination and disease status are independent He: vaccination and disease status are dependent Ho: vaccination and disease status are dependent Ha vaccination and disease status are independent

Answer 1

Step 1 As Null hypothesis always shows no relation between two variables the Null and alternate hypothesis are

Ho: vaccination and disease status are independent He: vaccination and disease status are dependent

Step 2

Vaccination status Vaccinated Not Vaccinated Total Diseased 59 76 135 Not Diseased 53 83 136 Total 112 159 271 Expected value Vaccinated Not Vaccinated Total Diseased 55.79 79.21 135.00 Not Diseased 56.21 79.79 136.00 Total 112.00 159.00 271.00

Total number of vaccinated and are diseased=Total of vaccinated*total no diseased/Total observations=112*135/271=

Step 3 Expected frequency of not vaccinated and diseased is 79.21

Step 5 degree of freedom =

(No of rows-1)* (No of columns-1)=(2-1)*(2-1)=1

Step 6 Critical value as per Excel formula =CHIINV(prob,d.f.)=CHiINV(0.005.1)=7.879

Step 7 Decision

Squared distances Body head/neck Total Diseased 0.18 0.13 0.31 Not Diseased 0.18 0.13 0.31 Total 0.37 0.26 0.63

Test statistic $X^{2}$ =0.63

P-value as per Excel formula=CHIDIST(x,d.f)=CHIDIST(0.63,1)=0.43

As P-value(0.43) is greater than alpha(0.005) we fail to reject the null hypothesis.

So we have enough evidence to prove that vaccination and disease status are independent.

Step 8

There is not significant evidence that vaccination and disease status are related.