Question

A survey wanted to determine what kind of game system was preferred by students. In a

survey of 150 students, 126 indicated that they preferred Xbox. Calculate and interpret a 99%

confidence interval for the proportion of all students who preferred Xbox.

Answer 1

The 99% Confidence interval for the proportion of students who preferred Xbox (P) is given by -

where, n is the sample size = 150

p is the sample proportion of students who preferred Xbox  

= 0.84

is the critical value of z for the two tailed test at 0.01 level of significance = 2.58 as obtained from the z table.

Putting all these values in the formula of confidence interval, we get,

= [ 0.763, 0.917]

Hence, we are 99% confident that the Proportion of students who preferred Xbox is between 0.763 and 0.917.