As part of a survey of a random sample of students, respondents were asked whether they were satisfied with the Students' Union Entertainments programme. Of the 109 respondents from the Arts Faculty 83 reported that they were satisfied with the Entertainments programme. Of the 116 respondents from the Business Faculty 97 reported that they were satisfied with the Entertainments programme.
(a) Construct a 90% confidence interval for the proportion of students in the Arts Faculty who are satisfied with the Entertainments programme.
(b) Construct a 90% confidence interval for the proportion of students in the Business Faculty who are satisfied with the Entertainments programme.
(c) Contrast the two confidence intervals.