Question

ive manufacturer wants to know the proportion of new car buyers who prefer foreign cars over domestic. Step 2 of 2: Suppose a sample of 2017 new car buyers is drawn. Of those sampled, 484 preferred foreign over domestic cars. Using the data, construct the 95% confidence interval for the population proportion of new car buyers who prefer foreign cars over domestic cars. Round your answers to three decimal places.

Answer 1

0.2305 ; 0.2495)

Explanation:

Sample size, n = 2017

Number who preferred foreign over domestic cars, x = 484

Phat = 484 / 2017 = 0.2399603 = 0.240

The confidence interval :

Phat ± Margin of error

Margin of Error = Zcritical * √(phat(1-phat)/n)

Zcritical at 95% = 1.96

1 - phat = 1 - 0. 240 = 0.76

Margin of Error = 1.96 * √((0.240*0.76)/2017) = 0.0095095

Confidence interval :

Lower boundary : 0.240 - 0.0095 = 0.2305

Upper boundary : 0.240 + 0.0095 = 0.2495

(0.2305 ; 0.2495)