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. ​b) How would the confidence interval change if the sample size had been 375 instead of 150​? ​(Assume the same sample​ proportion.) The new confidence interval would be ▼ The new confidence interval would be left parenthesis nothing comma nothing right parenthesis .

Answer 1

Solution:

Given,

Given a 98% confidence interval is (0.307 , 0.493)

Sample size used is n = 150

x = 60

Let denotes the sample proportion.

     = x/n = 60/150 = 0.4

Now ,

New sample size n = 375

Take same sample proportion = 0.4

Construct 98% confidence interval for p

c = 0.98

= 1- c = 1- 0.98 = 0.02

  /2 = 0.01

= 2.326 (use z table)

Now , the margin of error is given by

E = /2 *  

= 2.326 * [0.4 *(1 - 0.4)/375]

= 0.059

Now the confidence interval is given by

( - E)   ( + E)

(0.4 - 0.059)   (0.4 + 0.059)

0.341 0.459

(0.341 , 0.459)

The new confidence interval would be narrower than old.

The new confidence interval would be (0.341 , 0.459)