Question

Flu Vaccine: The Center for Disease Control (CDC) claims that the flu vaccine is effective in reducing the probability of getting the flu. They conduct a trial on 2000 people. The results are summarized in the contingency table below.

Observed Frequencies: O_i's

	Got	No
	Vaccine	Vaccine	Totals
Got Flu	20	21	41
No Flu	1280	679	1959
Totals	1300	700	2000

The Test: Test for a dependent relationship between getting the vaccine and getting the flu. Conduct this test at the 0.05 significance level.

(a) What is the null hypothesis for this test?

H₀: Getting the flu vaccine helps prevent the flu.H₀: Getting the flu vaccine and getting the flu are independent variables.     H₀: Getting the flu vaccine and getting the flu are dependent variables.

(b) What is the value of the test statistic? Round to 3 decimal places unless your software automatically rounds to 2 decimal places.

χ²

=

(c) Use software to get the P-value of the test statistic. Round to 4 decimal places unless your software automatically rounds to 3 decimal places.
P-value =

(d) What is the conclusion regarding the null hypothesis?

reject H₀fail to reject H₀    

(e) Choose the appropriate concluding statement.

We have proven that getting the flu vaccine prevents the flu.The evidence suggests that getting the flu vaccine and getting the flu are dependent variables.    There is not enough evidence to conclude that getting the flu vaccine and getting the flu are dependent variables.

Answer 1

The statistical software output for this problem is :

_H0: Getting the flu vaccine and getting the flu are independent variables.  

Test statistics = 4.840

P-value = 0.0278

reject H₀

The evidence suggests that getting the flu vaccine and getting the flu are dependent variables.