Problem 6 [Total 5 marks] The drug Ziac is used to treat hypertension. In a large clinical trial it was found that 32% of those in the placebo group experienced dizziness.
(a) [1 mark] Assuming that the same 32% proportion applies to subjects taking the drug, find the probability that among 20 drug users, exactly 6 have the side-effect.
(b) [1 mark] If 10 of the 20 drug users were to experience dizziness, find an exact 95% confidence interval for the proportion of drug users having dizziness. Would it appear that the proportion of drug users having dizziness is different from the 32% proportion? Why?
(c) [2 marks] In a subsequent clinical trial, it turned out that 4 out of 20 subjects taking the drug experienced the side effect. Carry out an exact hypothesis test at the 0.05 significance level to test that the true proportion of the drug users experiencing dizziness differs from 32%. State clearly the hypotheses and give the p-value.
(d) [1 mark] In the future, the researchers plan to collect more data to improve the accuracy of the current results. Compute the sample size required to obtain an approximate 95% confidence interval with half-width 0.05 for the true proportion.
1 answer