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	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.

Answer 1

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.