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. c) How would the confidence interval change if the confidence level had been 99​% 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

The width of confidence interval increases as confidence level increases

So new confidence interval would be wider

We have n = sample size = 150

X = number of yes response = 60

The sample proportion p^ = 60/150 = 0.40

The 99% confidence interval for population proportion

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

For a = 0.01 , Z​​​​​​a/2 = Z​​​​​​0.005 = 2.58

0.40-2.58*sqrt[0.40*0.60/150] < p <0.40+2.58*sqrt[0.40*0.60/150]

0.297 < p < 0.503

The new confidence interval would be ( 0.297 , 0.503)