Question

A survey of 150 students is selected randomly on a large university campus. They are asked if they use a laptop in class to take notes. The result of the survey is that 60 of the 150 students responded​ "yes." An approximate 98​% confidence interval is ​(0.307​, 0.493​). Complete parts a through d below. ​a) How would the confidence interval change if the confidence level had been 90​% instead of 98​%? The new confidence interval would be ▼ wider. narrower. The new confidence interval would be left parenthesis nothing comma nothing right parenthesis .

Answer 1

Sample proportion = 60 / 150 = 0.4

90% confidence interval for p is

- Z/2 * sqrt [ ( 1 - ) / n ] < p < + Z/2 * sqrt [ ( 1 - ) / n ]

0.4 - 1.645 * sqrt ( 0.4 ( 1 - 0.4) / 150 ] < p < 0.4 + 1.645 * sqrt ( 0.4 ( 1 - 0.4) / 150 ]

0.334 < p < 0.466

90% CI is ( 0.334 , 0.466 )

a)

The new confidence interval would be narrower

b)

The new confidence interval would be ( 0.334 , 0.466 )