Question

# Flu Vaccine: The Center for Disease Control (CDC) claims that the flu vaccine is effective in...

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: Oi'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.

(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.