Question

A student is considering publishing a new magazine aimed directly at owners of Japanese automobiles. He wants to estimate the fraction of cars in the United States that are made in Japan. The computer output to the right summarizes the results of a random sample of 50 autos. Explain carefully what it tells you.Choose the correct answer below. A. It is probably true that 42.1% of all cars in the United States are made in Japan. B. 42.1% of all cars in the United States are made In Japan. lib C. We are 95% confident that between 33.8% and 50.3% of cars in the United States are made in Japan. D. We don't know exactly what proportion of cars In the United States are made in Japan. but we know that it's within the interval 42.1 %t 1.96 x 4.2%. That is, ifs between 33.8% and 50.3%.

Answer 1

The right option is:

C. We are 95% confident that between 33.8% and 50.3% of cars in the United States are made in Japan.

Explanation:

The question is incomplete:

The output data is:

z-interval for the proportion 0.338<p(japan)<0.503

The right option is:

C. We are 95% confident that between 33.8% and 50.3% of cars in the United States are made in Japan.

As we are making an inference about the population proportion from one sample, we can not be 100% confident about the value of the population proportion.

As this is a 95% confidence interval, we can be 95% confident that the true proportion is within this interval.

The sample proportion is an estimator of the population proportion but it is unlikely to be the exact value for it.