Question

An industrial medical officer of a large factory wants to immunize the employees against influenza. Two vaccines A and B based on current viruses are available, but nobody knows which is preferable. From the workforce, 500 employees were selected and divided into two equal groups of 250 each. One group was immunized with vaccine A and the other was immunized with vaccine B in the first week of December. In the first week of the following March he examines the records he has been keeping to see how many employees got influenza.

(a) What is the variable observed on each employee? Is it an attribute or measurable?

(b) State the hypotheses in testing the efficacy of the two vaccines against influenza.

(c) By examining the records in March, the medical officer finds out 40 employees who received vaccine A got influenza. Whereas 25 of the employees who received vaccine B got influenza. Using the data, calculate the value of the test statistic and the p-value?

(d) Would you reject H0 or fail to reject H0 at 5% level of significance?

(e) What do you conclude about the efficacy of the vaccines against influenza?

(f) Which vaccine would you recommend?

Answer 1

solution:

let sample 1 is used for vaccination A and sample nol 2 is denoted for vaccination B

for sample 1:

number of person who got influenza after using vaccine A = 40

so

for sample 2:

number of person who got influenza after using vaccine B = 25

value of the pooled proportion is computed as

a) we have to count the number of employees whether they got influenza or not after vaccination. and these numbers are countable.

after that the respective proportion of both treatment are calculated.

b) null and alternative hypothesis:

since it is a right tailed test:

test statistics:

significance level = 0.05

critical value =

rejection region:

Z > 1.64

since , z=1.995 > , so rejecting the null hypothesis

conclusion;

there is sufficient evidence that vaccine A is providing high case of influenza after vaccination than using vaccine B.

so it can be concluded than vaccine B is efficient than vaccine A

f) so i will recommend vaccine B