Question

. A new vaccination is being used in a laboratory experiment to investigate whether it is effective. There are 252 subjects in the study. Is there sufficient evidence to determine if vaccination and disease status are related?

Vaccination Status     Diseased      Not Diseased       Total

Vaccinated                      51)               54)                    105)

Not Vaccinated    54)               73)                    147)

Total              (125)    (127)    ( 252)

State the null and alternative hypothesis.

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

Null hypothesis : H_o : vaccination and disease status are not related

Alternate hypothesis : H1 : vaccination and disease status are related

Observed Values (54 under Diseased; Not vaccinated ; wrongly entered; corrected to 74)

	Diseased	Not Diseased	Total
Vaccinated	51	54	105
Not Vaccinated	74	73	147
	125	127	252

Test Statistic :

E: Expected frequency

E :

	Diseased	Not Diseased	Total
Vaccinated	(125*105)/252	(127*105)/252	105
Not Vaccinated	(125*147)/252	(127*147)/252	147
	125	127	252

	Diseased	Not Diseased	Total
Vaccinated	52.0833	52.9167	105
Not Vaccinated	72.9167	74.0833	147
	125	127	252

O	E	O-E	(O-E)2	(O-E)2/E
51	52.0833	-1.0833	1.1736	0.0225
74	72.9167	1.0833	1.1736	0.0161
54	52.9167	1.0833	1.1736	0.0222
73	74.0833	-1.0833	1.1736	0.0158
			Total	0.0766

value of the test statistic = 0.077

degrees of freedom associated with the test statistic = ( number of rows -1 ) x Number of columns -1) =(2-1) x(2-1) = 1x 1=1

degrees of freedom associated with the test statistic = 1

Critical value of the test at the 0.01 level of significance for one degree of freedom = = 6.635

As test statistic : 0.077 is less tha critical value : 6.635; Fail to reject null hypothesist at the 0.01 level of significance.

Not enough evidence to reject that the vaccination and disease status are not related at the 0.01 level of significance.