(a)[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 a suitable sample.
(b)[1]
A suitable sample of 50 students is chosen and the number not wearing the correct uniform is recorded. This result is then used to perform a test at the $5\%$ significance level. State suitable null and alternative hypotheses.
(c)[5]
Use a binomial distribution to determine the probability of a Type I error. Your answer must be fully justified.
(d)[2]
In fact, 4 students out of the 50 are not wearing the correct uniform. State the conclusion of the test, with an explanation.
(e)[2]
State, with a reason, which error, Type I or Type II, may have occurred.