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	21	18	39
No Flu	1379	582	1961
Totals	1400	600	2000

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

(a) What is the test statistic? Round your answer to 3 decimal places.

χ² =  

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

reject H₀

fail to reject H₀    
(c) 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

applying chi square test:

Expected	Ei=row total*column total/grand total	Vaccine	no Vaccine	Total
	Get flu	27.30	11.70	39
	No flu	1372.70	588.30	1961
	total	1400	600	2000
chi square    χ2	=(Oi-Ei)2/Ei	Vaccine	no Vaccine	Total
	Get flu	1.4538	3.3923	4.846
	No flu	0.0289	0.0675	0.096
	total	1.483	3.460	4.943

a)

test statistic X² =4.943

b)

reject H₀

c)

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