Question

Erica has a swimming pool at her house. Once a year she purchases a 50-pound bucket of chlorine pellets from an online company. Out of curiosity she weighs the bucket and finds that it only weighs 46.2 pounds. She purchases 4 more 50-pound buckets, giving her an SRS of size 5. The mean weight of the 5 buckets is 48.5 pounds. She suspects that the company is cheating the customers. She uses her data to test the hypotheses H0: \muμ = 50 pounds versus Ha: \muμ < 50 pounds. The P-value of her test is 0.0851. What decision should she make and what type of error could she make as a result of her decision?

Answer 1

Answer:

She should fail to reject the null hypothesis. She could make a Type II error, meaning she fails to find convincing evidence that the true mean weight of the 50-pound buckets is less than 50 pounds when in reality it is.

Explanation:

Answer 2

Answer:

Explanation:

The correct answer is (D).

Because the P-value of 0.0851 is greater than α = 0.05, she should fail to reject the null hypothesis. Because she failed to reject the null hypothesis it is possible that she has made a Type II error, meaning, it is possible that the true mean is less than 50 pounds, but she failed to find convincing evidence to make this conclusion.