Nikki is investigating the views of students at her school about the school sports facilities. She plans to give a survey to a sample of students.

Nikki’s friend says, “This survey is about sports facilities, so you should choose a sample of students from the school sports teams.”

(a) State, with a reason, whether you agree with Nikki’s friend. [1]

Nikki chooses an appropriate random sample of 60 students. She finds that 45 of these students think that the sports facilities are good.

(b) Calculate an approximate 95% confidence interval for the proportion of students who think that the sports facilities are good. [3]

For a different investigation, Nikki uses another large random sample to calculate a 99% confidence interval and an \(x\)% confidence interval. The width of the 99% confidence interval is double the width of the \(x\)% confidence interval.

(c) Calculate the value of \(x\). [4]