Question

When 500 college students were surveyed, 30% said that they own their car. Construct a 95% confidence interval for the proportion of college students who say they own their cars. DON'T JUST GIVE THE ANSWER - SHOW WORK AND EXPLAIN YOUR PROCESS EACH STEP OF THE WAY SO THAT I CAN FOLLOW WHAT YOU DID AND CHECK YOUR WORK

Answer 1

Solution

Given: n=Total number of college students surveyed=500

x=The number of students who own car=30%*500=150

The estimated population proportion,p=x/n=150/500=0.3

The given confidence level is 95% then =1-CL=1-0.95=0.05=0.05/2=0.025

From the z distribution table z=z0.025=1.96

The below screenshot is for your reference.

The confidence interval formula is given as follows:

pz0.025p(1-p)/n

0.3(1.960.3(1-0.3)/500)

0.30.04

(0.26,0.34)

Therefore 95% confidence interval for the proportion of college students who say they own their cars lies between 26% and 34%.