Answered

Westonci.ca offers quick and accurate answers to your questions. Join our community and get the insights you need today. Discover the answers you need from a community of experts ready to help you with their knowledge and experience in various fields. Discover detailed answers to your questions from a wide network of experts on our comprehensive Q&A platform.

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.

Sagot :

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:

[tex]H_0: p = 0.53[/tex]

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

[tex]H_1: p > 0.53[/tex].

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 https://brainly.com/question/16313918

We hope our answers were useful. Return anytime for more information and answers to any other questions you have. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Thank you for using Westonci.ca. Come back for more in-depth answers to all your queries.