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 infavour 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∑x=35.9 ∑x2=186.19 Calculate.i The sample mean ii.The sample variance iii.A 90%confidence interval for the population mean