In a poll to estimate the prime minister's popularity, each person in a random sample of 1000 voters was asked to agree with one of the following statements: 1. The prime minister is doing a good job. 2. The prime minister is doing a poor job. 3. I have no opinion. A total of 550 respondents selected the first statement, indicating they thought the prime minister was doing a good job. a.Construct a 95% confidence interval for the proportion of respondents who feel the prime minister is doing a good job. to (2 marks) b.On the basis of your interval in part (a), is it reasonable to conclude that a majority (more than half) of the population believes the prime minister is doing a good job? (2 marks)