Question

A representative of a car manufacturer in the United States made the following claim in a news report. "Ten years ago, only 53 percent of Americans owned American-made cars, but that figure is significantly higher today." A research group conducted a study to investigate whether the claim was true. The group found that 56 percent of a randomly selected sample of car owners in the United States owned American-made cars. A test of the appropriate hypotheses resulted in a p-value of 0.283. Assuming the conditions for inference were met, is there sufficient evidence to conclude, at the significance level of a = 0.05, that the proportion of all car owners in the United States who own American-made cars has increased from what it was ten years ago?
i. Yes, because 0.56 > 0.53.
ii. Yes, because a reasonable interval for the proportion is 0.56 ± 0.283.
iii. Yes, because 0.56 - 0.53 = 0.03 and 0.03 < 0.05.
iv. No, because 0.283 < 0.53.
v. No, because 0.283 > 0.05.

Answer 1

According to the p-value, the correct option regarding the decision of the test hypothesis is:

v. No, because 0.283 > 0.05.

What are the hypothesis tested?

At the null hypothesis, we test if the proportion is still of 0.53, that is:

$H_0: p = 0.53$

At the alternative hypothesis, we test if it has increased, that is:

$H_1: p > 0.53$.

What is the decision according to the p-value?

• If p-value > significance level, we do not reject the null hypothesis.

• If p-value < significance level, we reject the null hypothesis.

In this problem, the p-value is of 0.283 > 0.05, hence there is not sufficient evidence to conclude, at the significance level of a = 0.05, that the proportion of all car owners in the United States who own American-made cars has increased from what it was ten years ago, which means that option V is correct.

More can be learned about p-values at brainly.com/question/16313918