Question

A new vaccination is being used in a laboratory experiment to investigate whether it is effective. There are 266 subjects in the study. Is there sufficient evidence to determine if vaccination and disease status are related? Vaccination Status Diseased Not Diseased Total Vaccinated 53 57 110 Not Vaccinated 73 83 156 Total 126 140 266

Step 1 of 8: State the null and alternative hypothesis.

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.

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 0.01 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 0.01 level of significance.

Step 8 of 8: State the conclusion of the hypothesis test at the 0.01 level of significance.

Answer 1

Observed table ! Not diseased Total Diseased 53 S] 110 vaccinated Not vaccinated 73 83 I56 Total 266 126 140 Expected table i Diseased Not diseased 140XIO 57.895 266 vaccinated 126 X110 52.IOS 266 126 x 156 73.89S 8.2.105 Not vaccinated 140X15C 266 266 The null and alternative hypotheses are vaccination and disease status are not related Hi; vaccination and disease status are related. Test statistic + 4. [Coi-E;)? + Ei (53-52.105)? (57-57-895)2 (73-73-895)2 $2.105 570895 73.895 C83-82.10532 82-105 72: 0.015 + 0.011 + 0.014 + 0.01 0.05 (r-CC-1) = (2-1)(2-1)=1 degrees of freedom critical value at x=0.01 with df = 1 X² - critical Xo.ch 6.635 since, x2 < Xãritical, we fail to reject the null bypothesis There is not sufficient evidence to conclude that vaccination and disease status are related .