Question

Thalidomide is a tranquilizer that was prescribed in the late 1950’s and early 1960’s to pregnant women, with the devastating result of over 12,000 birth defects in 48 countries before it was banned in 1962. (It was never sold in the United States.) Since then, the drug has reappeared as a possible solution to a number of medical problems. The U.S. National Institutes of Health announced on 31 October 1995 the results of a study in 30 hospitals of the effectiveness of thalidomide in healing mouth ulcers in AIDS patients. In the study, which was chaired by Dr. Jeffrey Jacobson of the Bronx Veteran Affairs Medical Center and the Mount Sinai School of Medicine in New York, it was found that 14 out of 23 patients who received thalidomide had their ulcers heal compared to 1 out of 22 patients who received a placebo. As a result of these early trial outcomes, the researchers suspended the trial giving thalidomide to all the patients in the study. THIS IS ALL THE INFO GIVEN.

1. Find a 90% confidence interval for the difference in proportion of healing assuming that both samples are simple random samples and independent of each other.
2. Conduct the appropriate large-sample test of significance. Discuss your results and compare your conclusion with the decision of the researchers.
3. By hand, draw a bar graph depicting the sample proportions of healing. Add a whisker to the top of each bar to denote the standard error of the sample proportion.  DO NOT SUBMIT.
4. Examine the bar graph you produced for part (a). Briefly comment on whether there appears to be a difference in proportions.
5. Conduct the appropriate hypothesis test for a two-by-two contingency table and report the P-values for Fisher’s exact test and the asymptotic chi-square distribution approximation for this test. Compare these results with your answer to part (b) in Exercise 1.

Answer 1

90% confidence interval for the difference of proportion of patients who got healed by Thalidomide and and by placebo is given by

For 90% confidence interval

Hence 90% confidence interval for difference of proportion is

(0.331986,0.794496)

Large sample test of significance

   

Z critical value= 2.33

Reject the null hypothesis that there is no significant difference in the proportion.and accept that the proportion of patients who recover using Thalidomide is more

	Thalidomide	Placebo	Total
Healed	14	1	15
Do not heal	9	21	30
Total	23	22	45

Thalidomide is not effective in healing.

Thalidomide is effective in healing.

Oi	14	9	1	21
Ei	5.23188	2.6159	5.46969	2.734848

Critical value with 1 degree of freedom = 2,7055 (confidence level 90%)

Hence we reject the null hypothesis and conclude that Thalidomide is effective in healing.