Question C

Table 2: Number of Prime Ministers of Country J classified under Duration of Stay in Office, Glasses- wearing and Alma Mater Wear Longer Stay in Office Shorter Stay in Office Glasses? Capital Other Capital Other Total University Universities University Universities Yes 12 14 12 32 70 No 23 16 3 13 55 Total 35 30 15 45 125 (b) (1.5 marks) Amos also wondered if wearing glasses affected the stay in office by the prime minister. This meant that he would like to know, among those prime ministers who wore glasses, what percentage of them had longer stay in office. Construct a 95% confidence interval for PIG, the proportion of glasses-wearing prime ministers who had longer stay in office. (In doing so, please use your estimate of pic to work out the standard deviation for PLG.) Give your answer correct to 4 decimal places. (c) (2 marks) Charlotte would like to quantify with some level of certainty Plong, the proportion of prime ministers who had longer stay in office. At least how many more prime ministers needed to be considered if Charlotte was to estimate Plong to be within 0.02 of its true value with a probability of 0.95? You may assume that the true Plong is equal to Charlotte's estimate based on the collected data