Question

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

Step 2 of 2 :  

Suppose a sample of 510new car buyers is drawn. Of those sampled, 142 preferred foreign over domestic cars. Using the data, construct the 85% confidence interval for the population proportion of new car buyers who prefer foreign cars over domestic cars. Round your answers to three decimal places. previous answer was .278

Answer 1

Solution :

Given that,

n = 510

x = 142

Point estimate = sample proportion = = x / n = 142 / 510 = 0.278

1 - = 1 - 0.278 = 0.722

At 85% confidence level

= 1 - 85%

=1 - 0.85 =0.15

/2 = 0.075

Z/2 = Z_0.075 = 1.44

Margin of error = E = Z _{/ 2} * (( * (1 - )) / n)

= 1.44 (((0.278 * 0.722) / 510 )

= 0.029

A 85% confidence interval for population proportion p is ,

± E

= 0.278 ± 0.029

= ( 0.249, 0.307 )