In a forthcoming election of student's welfare association officers, an official wanted to know the students who preferred voting for the female representative to the male one for the chairperson post. He surveys 350 students and finds that 188 preferred the female candidate.

(a) Using a 99% confidence level, calculate a confidence interval estimate for the proportion of all students who preferred the female candidate as chairperson. Show your working and give your answer to four decimal places. Interpret the confidence interval

(b) Suppose the official wants to test whether the proportion of all students who prefer the female candidate as chairperson is different from 62%. (i) Write the null and alternative hypotheses for this test.

(i) Write the null and alternative hypotheses for this test.

(ii) Define the term "Type I error". What is a Type I error in the context of the hypothesis test in part (b)(i)?

(c)Based on the 99% confidence interval in part (a), can you conclude that the proportion of all students who prefer voting a female chairperson has changed from 0.62? Give reason(s) to support your answer