Question

5. 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 21 18 39 No Flu 1379 582 1961 Totals 1400 600 2000 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 independent variables. H0: Getting the flu vaccine helps prevent the flu. H0: Getting the flu vaccine and getting the flu are dependent 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 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

The Expected value data are in the table below. Each Cell = Row total * Column Total/N. N = 2000

Observed
	Got Vaccine	No Vaccine	Total
Got Flu	21	18	39
No Flu	1379	582	1961
Total	1400	600	2000
Expected
	Got Vaccine	No Vaccine	Total
Got Flu	27.30	11.70	39
No Flu	1372.70	588.30	1961
Total	1400	600	2000

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(a) The Null Hypothesis: H0: getting the flu Vaccine and getting the flu are independent variables

(b) The Test Statistic:

Number	Observed	Expected	(O-E)	(O-E)2	(O-E)2/E
1	21	27.30	-6.30	39.69	1.4538
2	1379	1372.70	6.30	39.69	0.0289
3	18	11.70	6.30	39.69	3.3923
4	582	588.30	-6.30	39.69	0.0675
Total					4.9425

= 4.943 9Rounding to 3 decimal places)

(c) The degrees of freedom = (r-1) * (c-1) = 1. The p value = 0.0262

(d) Since p value is > (0.01), Fail to Reject H0.

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