Question

A car manufacturer randomly samples and interviews 1,000 consumers in a target market. Of the 1,000 interviewed, 93 indicated that they are likely to purchase a car from this manufacturer.

Keep as many decimals as possible in your computations, but please enter the final answers to three decimal places.

-) Define the parameter p of interest in full context.

-) Compute the value of the statistic pˆ.

-) Compute the 95% confidence interval estimating p.

Select one:

(0.069, 0.117)

(0.117, 0.069)

(0.075, 0.111)

(0.111, 0.075)

-) Interpret the confidence interval in full context.

-) Using this interval, would you conclude that the proportion of consumers likely to purchase a car from this manufacturer differs from 10%? Why or why not?

Answer 1

A car manufacturer randomly samples and interviews 1,000 consumers in a target market. Of the 1000 interview, 93 indicated that they are likely to purchase a car from this manufacturer.

Let p be the population proportion of consumer's who are likely to purchase a car from the car manufacturer.

The estimate of the population proportion is given by

From the confidence interval, we are 95% sure that the true population proportion consumers who are likely to purchase a car from this manufacturer contains in the calculated confidence interval.

Since the confidence interval contains the value of population proportion p=0.10, we do not have enough evidence to claim that the proportion of consumers who are likely to purchase a car from this manufacturer differs from 10%.