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 3000 people. The results are summarized in the contingency table below.

Observed Frequencies: O_i's

	Got	No
	Vaccine	Vaccine	Totals
Got Flu	33	32	65
No Flu	1917	1018	2935
Totals	1950	1050	3000

The Test: Test for a dependent relationship between getting the vaccine and getting the flu. Conduct this test at the 0.01 significance level.

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

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

(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 H₀ fail 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

(a)
Correct option:

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

(b)

Expected Frequencies are got as follows:

	Got vaccine	No vaccine	Total
Got flu	1950X65/3000=42.2500	1050X65/3000=22.7500	65
No flu	1950X2935/3000=1907.7500	1050X2935/3000=1027.2500	2935
Total	1950	1050	3000

Test Statistic is calculated as follows:

Observed (O)	Expected (E)	(O - E)2/E
33	42.2500	2.0251
32	22.7500	3.7610
1917	1907.7500	0.0448
1018	1027.2500	0.0833
Total = =		5.914

(c)

ndf = (r - 1) X (c - 1)

= (2 - 1) X (2 - 1)

= 1

By Technology, P - value = 0.0150

(d)

Correct option:

fail to reject H₀  

(e)
Correct option:

There is not enough evidence to conclude that getting the flu vaccine and getting the flu are dependent variables.