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A researcher is interested in determining whether taking additional vitamin C helps prevent the common cold. A randomised experiment was conducted to address this question. The study randomly allocated 279 people to either a group where vitamin C supplements were given, or a group where a placebo pill was given. These peeple were monitored and the numbers of those who got or did not get a cold were recorded. The results are summarised below: Got a cold Did not get a cold Placebo 31 109 i. Give a 95% condence interval for the difference in the probabilities of getting a cold between the vitamin C and the placebo groups. ii. Carry out an appropriate hypothesis test at the 5% signicance level to determine whether the probability of getting a cold is lower in the vitamin C 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 ndings. iii. State any assumptions you made in part ii. iv. On the basis of the data alone, would you conclude that a vitamin C pill reduces the chances of getting a cold? Provide an explanation with your