Question

Step 2 of 8: Find the expected value for the number of subjects who are vaccinated and are diseased. Round your answer to one decimal place.

A new vaccination is being used in a laboratory experiment to investigate whether it is effective. There are 235 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 58 112 Not Vaccinated 66 57 123 Total 120 115 235 Copy Data Step 1 of 8: State the null and alternative hypothesis.

Step 3 of 8: Find the expected value for the number of subjects who are not vaccinated and are not diseased. Round your answer to one decimal place.

Step 4 of 8: Find the value of the test statistic. Round your answer to three decimal places.

Step 5 of 8: Find the degrees of freedom associated with the test statistic for this problem.

Step 6 of 8: Find the critical value of the test at the 0.1 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 0.1 level of significance.

Step 8 of 8: State the conclusion of the hypothesis test at the 0.1 level of significance.

Answer 1

Total Diseased Not diseased 54 58 Vaccination status Vacinated Not Vacunated Total 66 52 123 235 120 IS 1) Ho: There is no no relationship betwerh vacunation and disecue status. Hi : The is a relationship between Vaccination and diseaue status Expected value for not vacinated and not diseased 60.19 123 X 115 235 2) Expected value for vacinated and are diseased. 57.19 112 X120 235 Expected value for and diseased not vacunated 6 2.81 123 x 120 235 Expected value for vacinated and not diseased 112 7 115 54081 235 CS Scanned with CamScanner

4) Test statistic is, Elo; -ei) Oi uency observed frequen ei = expected frequency ei Z 54-57.19 )? (58 - 54.81). 54.8) 57.19 2 +(66-62.81) 62.81 (57-60.13) 60.19 0.18 + oolg toolt tool7 X こ 0.695 5 degrees of treeeling (2-1) X (2-1) = 1 where r= no. of rows c = no. of columns 6) x² - critical value - 2.70G 7) since x² calculated < Co.ggs) Hence fail to reject the x²-critical value ( 2,706) null hypothesis. 8) Thus, there is not sufficient evidence to conclude that vaidination and disease are related. CS Scanned with CamScanner