Question

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

Step 1 of 2:

Suppose a sample of 390 new car buyers is drawn. Of those sampled, 105 preferred foreign over domestic cars. Using the data, estimate the proportion of new car buyers who prefer foreign cars. Enter your answer as a fraction or a decimal number rounded to three decimal places.

Step 2 of 2:

Suppose a sample of 390 new car buyers is drawn. Of those sampled, 105 preferred foreign over domestic cars. Using the data, construct the 80% 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

Solution :

Given that,

n = 390

x = 105

(a)

Point estimate = sample proportion = = x / n = 105 / 390 = 0.269

1 - = 1 - 0.269 = 0.731

(b)

At 80% confidence level the z is ,

= 1 - 80% = 1 - 0.80 = 0.20

/ 2 = 0.20 / 2 = 0.10

Z_/2 = Z _0.10 = 1.28

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

= 1.28 * (((0.269 * 0.731) / 390)

= 0.029

A 80% confidence interval for population proportion p is ,

- E < p < + E

0.269 - 0.029 < p < 0.269 + 0.029

0.240 < p < 0.298

The 95% confidence interval for the population proportion p is : (0.240 , 0.298)