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

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

Observed Frequencies: Oi's

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 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.

2

=  

(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.

Got No Vaccine Vaccine Totals Got Flu   15     30     45   No Flu   985     970     1955   Totals   1000     1000     2000  

Explanation / Answer

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

(b) chi-square=sum((O-E)2/E)=5.12 with 1 df

(c) P-value=0.0237 (using ms-excel command =CHIDIST(5.12,1) )

(d) rejcet H0, as p-value is less than alpha=0.05

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

Got No Vaccine Vaccine Totals Got Flu   15     30     45   No Flu   985     970     1955   Totals   1000     1000     2000   observed(O) Expected Expected(E) (O-E) (O-E)2/E 15 45*1000/2000 22.5 -7.5 2.5 30 45*1000/2000 22.5 7.5 2.5 985 1955*1000/2000 977.5 7.5 0.057545 970 1955*1000/2000 977.5 -7.5 0.057545 sum= 2000 2000 0 5.11509

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