Question

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

Step 1: Suppose a sample of 958 new car buyers is drawn. Of those sampled, 383 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: Suppose a sample of 958 new car buyers is drawn. Of those sampled, 383 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.

Lower endpoint: ? Upper endpoint: ?

Answer 1

Step 1 )

Sample proportion = 383 / 958 = 0.400

Step 2)

95% confidence interval for p is

- Z * sqrt( ( 1 - ) / n) < p < + Z * sqrt( ( 1 - ) / n)

0.400 - 1.96 * sqrt( 0.400 * 0.600 / 958 ) < p < 0.400 + 1.96 * sqrt( 0.400 * 0.600 / 958 )

0.369 < p < 0.431

Lower endpoint = 0.369

Upper endpoint = 0.431