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 768 new car buyers is drawn. Of those sampled, 192 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 768 new car buyers is drawn. Of those sampled, 192 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

Answer: step 1: 0.25 or 1/4

Step 2: 192.047 or 191.953

Explanation:

Given Data;

Sample size, n = 768

Number of people who preferred foreign cars over domestic, x = 192

Therefore;

proportion of new car buyers who prefer foreign cars.

P = x/n

Inputting the value of x and n in the equation

P = 192 / 768

P = 0.25 or 1/4

The proportion of the new car buyers who preferred foreign over domestic cars is 0.25 or 1/4

Step 2:

n = 768

x = 192

80% confidence interval

X ± Z s/ √ (n)

192 ± 1.282 * 1/ 27.12

192 ± 0.0473

= 192.047 or 191.953