Question

An automotive Manufacture wants to know the proportion of new car buyers who prefer foreign cars over domestic.

Step 2 of 2: suppose a sample of 2851 new car buyers is drawn. Of those sampled, 684 preferred for an over domestic cars. Using the data, construct the 98% confidence interval for the population proportion of new car buyers who prefer foreign cars over domestic. Round your answer to three decimal places.

Answer 1

Sample proportion = (number of people who preferred for an over domestic car)/(total number of people surveyed) = (684/2851)=0.24

Sample size n= 2851

We need to find the confidence interval for the 98% confidence interval, so the critical z score corresponding to 98% confidence interval is given as

z score = 2.33

Formula for the confidence interval is given as  

CI =

setting the given values, we get

CI =

on solving, we get

CI =

So, the required 98% confidence interval for the population proportion of new car buyers who prefer foreign cars over domestic is (0.2214,0.2586)