Question 3 (a) A study of the population of female tea drinkers showed that out of a sample of 165 female tea drinkers surveyed, 46 said their tea of choice is a herbal tea. Carry out a hypothesis test to determine if this gives evidence that more than 20% of the population of female tea drinkers prefer a herbal tea, i.e test the hypothesis p > 0.20, at significance level a=0.05. [6 Marks] (b) For the herbal tea drinkers in the female sample their tea of choice was recorded as one of five categories, giving the following summary counts. Observed Herbal Tea: Frequency Chamomile 13 Rooibos Peppermint 2 Ginger 14 Other Total 46 Use the sample observations to test whether the population of all herbal tea drinkers in the female population have an equal versus unequal distribution of proportions across these types of herbal tea, testing at significance level o=0.05. Include statements of the null and alternative hypotheses being tested, in terms of p1, p2, p3, p4, ps, the proportions of the population for each of the five categories. Include calculation of the value of the appropriate test statistic, the rejection region and a conclusion. [8 Marks] (c) In order to compare the proportion of herbal tea drinkers between the female and male tea drinking populations, both female and male samples were surveyed. Out of a sample of 165 female tea drinkers surveyed, 46 said their tea of choice is a herbal tea. Out of a sample of 126 male tea drinkers surveyed, 15 said their tea of choice is a herbal tea. Using these statistics calculate and interpret a 95% Confidence Interval for p1 - p2, the difference in proportions between the two populations. Does this indicate that there is a significant difference? Give a reason for your answer. [6 Marks]