A researcher is interested in determining whether a particular pill provides effective treatment for stomach pain. A randomised experiment was conducted to address this question. The study randomly...

A researcher is interested in determining whether a particular pill provides
effective treatment for stomach pain. A randomized experiment was conducted to address this question. The study randomly allocated 200 people to either a group where the pill was administered or a group where a placebo pill was given. These people were monitored and the numbers of those who got better (or did not) were recorded. The results are summarised below:

Extracted text: A researcher is interested in determining whether a particular pill provides effective treatment for stomach pain. A randomised experiment was conducted to address this question. The study randomly allocated 200 people to either a group where the pill was administered, or a group where a placebo pill was given. These people were monitored and the numbers of those who got better (or did not) were recorded. The results are summarised below: Did not get better Got better Pill 21 74 Placebo 50 55 i. Give a 95% confidence interval for the difference in the probabilities of getting better from stomach pain between those who took the pill and the placebo group. ii. Carry out an appropriate hypothesis test at the 5% significance level to determine whether the probability of getting better is higher in the pill group, compared to the probability in the placebo group. State the test hypotheses, and specify your test statistic and its distribution under the null hypothesis. Comment on your findings. iii. State any assumptions you made in part ii. iv. On the basis of the data alone, would you conclude that the particular pill increases the chances of getting better from stomach pain? Provide an explanation with your anSwer.