7.4 An experiment is performed in a medical clinic to determine if taking vitami

Question

7.4 An experiment is performed in a medical clinic to determine if taking vitamin C pills has any effect on preventing colds in the winter. Twins are enrolled in the study and one twin from each pair takes vitamin C every day for a month while the other twin takes a placebo pill. The subjects are observed for one month to determine if they develop colds. Vitamin C Group Cold No Cold Cold 2 No Cold 4 Control Group 18 (a) Test Ho: P1 = P2 versus Hai p1 p2, where pl and P2 are the probabilities of getting a cold for the vitamin C group and the control group, respectively. Use a 0.05. (b) Another researcher presents a table from an independent experiment similar to the one described above, except it was performed during the summer. In this experiment, the frequencies in the above table are 20, 11,4, and 180 (instead of 2, 11,4, and 18). This researcher claims that, since his experiment used more twin-pairs, his experiment resulted in stronger evidence that vitamin C helps prevent colds. Do you agree? Why or why not?

Explanation / Answer

H0: p1=p2

H1: p1#p2

a)

b)

Observed Vitamin C Group Total Cold No Cold Control Group Cold 2 11 13 No Cold 4 18 22 Total 6 29 35 Expected Vitamin C Group Total Cold No Cold Control Group Cold 2.228571429 10.77142857 13 No Cold 3.771428571 18.22857143 22 Total 6 29 35 (Obs-Exp)^2/Exp Vitamin C Group Total Cold No Cold Control Group Cold 0.023443223 0.004850322 0.028293546 No Cold 0.013852814 0.002866099 0.016718913 Total 0.037296037 0.007716422 0.045012459 Critical chisquare value is 3.84145882 and hence we should not reject the null hypothesis

b)

Observed Vitamin C Group Total Cold No Cold Control Group Cold 20 11 31 No Cold 4 180 184 Total 24 191 215 Expected Vitamin C Group Total Cold No Cold Control Group Cold 3.460465116 27.53953488 31 No Cold 20.53953488 163.4604651 184 Total 24 191 215 (Obs-Exp)^2/Exp Vitamin C Group Total Cold No Cold Control Group Cold 79.05186297 9.933218383 88.98508135 No Cold 13.31852039 1.673531358 14.99205175 Total 92.37038336 11.60674974 103.9771331 Critical chisquare value is 3.84145882 and hence we should reject the null hypothesis The researcher's claims are correct

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