A survey of 50 students found that 60% are happy with the quality of food at the school canteen.

(a) Construct a 90 percent confidence interval for the population proportion of students who are happy with the quality of food at the canteen. Give an interpretation of your result. [5 marks]

(b) Test the hypothesis, at the 10% significance level, that the true proportion is 50% against the alternative that majority of students are happy with the quality of food? Is the conclusion consistent with the result in (a)? [7 marks]

(c) Find the probability of committing a Type I error in the hypothesis test in (b). [3 marks]