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 2000 people. The results are summarized in the contingency table below.

Observed Frequencies: Oi's

 Got No Vaccine Vaccine Totals Got Flu 15 30 45 No Flu 985 970 1955 Totals 1000 1000 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 dependent variables.      H0: Getting the flu vaccine and getting the flu are independent 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.

Ans:

a)

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

b)

 Observed(fo) Got Vaccine No Vaccine Totals Got Flu 15 30 45 No Flu 985 970 1955 Totals 1000 1000 2000 Expected(fe) Got Vaccine No Vaccine Totals Got Flu 22.50 22.50 45 No Flu 977.50 977.50 1955 Totals 1000 1000 2000 chi square=(fo-fe)^2/fe Got Vaccine No Vaccine Totals Got Flu 2.500 2.500 5.000 No Flu 0.058 0.058 0.115 Totals 2.558 2.558 5.115

Test statistic:

Chi square=5.115

c)DF=(2-1)*(2-1)=1

p-value=CHIDIST(5.115,1)=0.0237

d)

As,p-value is less than 0.05, we reject the null hypothesis.

e)

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