A statistics instructor is interested in the ability of students to assess the difficulty of a test they have taken.A random sample of eight students was asked to predict this average score.Their predictions were 72,83,78,65,69,77,81,71.

a) What is the interval estimation of population prediction mean with level of confidence 90%?To construct the confidence interval, what assumption about population is needed?(14 marks)

b) Describe how the width of 90% confidence interval change if

(1) the sample prediction mean increases (2 marks)

(2) the sample standard deviation increases(2 marks)

(3) the sample standard deviation increases(2 marks)

(4) the margin of error increases(2 marks)

(5) the sample size increases(2 marks)

c) How large a sample of students would be needed in order to estimate the population prediction mean within 2 with 85% confidence? (5 marks)