The results of a trial involving an experimental vaccine for children are shown

Question

The results of a trial involving an experimental vaccine for children are shown below. Vaccine treatment Placebo Developed flu 20 104 Did not develop flu 1140 408 a. State the relevant null and alternative hypotheses. b. Conduct the appropriate test and state a conclusion. Use a significance level of 0.01 a. Determine the null and alternative hypotneses. Choose the correct answer below. 0 A. Ho: Treatment method and flu development have non-equal proportions. B. Ho: Treatment method is independent of flu development. ° C. Ho. Treatment method and flu development have equal proportions. 0 D. Ho: There is a relationship between treatment method and development of flu. HA: Treatment method and flu development have equal proportions. HA: There is a relationship between treatment method and development of flu. HA: Treatment method and flu development have non-equal proportions. HA: Treatment method is independent of flu development. b. Calculate the test statistic. X2-U (Round to three decimal places as needed.)

Explanation / Answer

(a) Option B

(b)

2 = 178.753

p- value = 0

Reject Ho. The variables are dependent.

Chi-square Contingency Table Test for Independence    Flue   No Flue   Total   Vaccine Observed   20 1140 1160 Expected   86.03 1073.97 1160.00 O - E   -66.03 66.03 0.00    (O - E)² / E   50.68 4.06 54.74 Placebo Observed   104 408 512 Expected   37.97 474.03 512.00 O - E   66.03 -66.03 0.00 (O - E)² / E   114.82 9.20 124.02 Total Observed   124 1548 1672 Expected   124.00 1548.00 1672.00 O - E   0.00 0.00 0.00 (O - E)² / E   165.50 13.26 178.75 178.753 chi-square 1 df 9.07E-41 p-value

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