8 At a certain large school it was found that the proportion of students not wearing correct uniform was 0.15 . The school sent a letter to parents asking them to ensure that their children wear the correct uniform. The school now wishes to test whether the proportion not wearing correct uniform has been reduced.

1. It is suggested that a random sample of the students in Grade 12 should be used for the test. Give a reason why this would not be an appropriate sample.
   A suitable sample of 50 students is selected and the number not wearing correct uniform is noted. This figure is used to carry out a test at the 5\% significance level.
2. State suitable null and alternative hypotheses.
3. Use a binomial distribution to find the probability of a Type I error. You must justify your answer fully.
4. In fact 4 students out of the 50 are not wearing correct uniform. State the conclusion of the test, explaining your answer.
5. State, with a reason, which of the errors, Type I or Type II, may have been made.
   If you use the following lined page to complete the answer(s) to any question(s), the question number(s) must be clearly shown.