Question

Suppose that a company selling flu vaccines says that it’s effective if fewer than 20% of all those who get a flu shot actually become sick with the flu. Let p = fraction of people who have been given the flu shot and become sick anyway. You want to test the following:

$Adapt_372.png$

If 75 of 300 people given the vaccine also get sick from the flu, what would you conclude given α = 0.05?

a) We fail to reject Ho, meaning that the flu vaccine is effective.

b) We fail to reject Ho, meaning that flu vaccine is ineffective.

c) We reject Ho, meaning that the flu vaccine is effective.

d) We reject Ho, meaning that flu vaccine is ineffective.

Answer 1

Po = 0.2


n = 300
P = X / n = 75/300 = 0.25

Test Statistic :-
$Z = ( P - P_{0}) / ( \sqrt{(P_{0} * q_{0})/n})$

Z = 2.1651

Z (0.25-0.2)(0.2 0.8)/300)

Test Criteria :-
Reject null hypothesis if $Z > Z_{\alpha}$

Za 20.00 1.6449

$Z > Z_{\alpha}$ = 2.1651 > 1.6449, hence we reject the null hypothesis
Conclusion :- We Reject H0

Decision based on P value
P value = P ( Z > 2.1651 )
P value = 0.0152
Reject null hypothesis if P value <
Since P value = 0.0152 < 0.05, hence we reject the null hypothesis
Conclusion :- We Reject H0

a-0.05

d) We reject Ho, meaning that flu vaccine is ineffective.