a) A college principal decides to consult the students about a proposed change in the time of lectures. She finds that out of a random sample of 80 students, 57 are in favour of the change.

i. Calculate a 95 % confidence interval for the proportion of students who are not in favour of the change.

ii. State the effect on the width of such a confidence larval when the confidence level is increased.

b) A random variable of 7 independent observations of a normal variable gave = 35. 9 2 = 186.19

Calculate i. The sample mean ii. The sample variance iii. A 90% confidence interval for the population mean