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:
μ
μ = 50 pounds versus Ha:
μ
μ < 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?

(A) She should reject
H
0
H
0
​ . She could make a Type I error, meaning she finds convincing evidence that the true mean weight of the 50-pound buckets is less than 50 pounds when in reality it is not.
(B) She should reject
H
0
H
0
​ . 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.
(C) She should fail to reject
H
0
H
0
​ . She could make a Type I error, meaning she finds convincing evidence that the true mean weight of the 50-pound buckets is less than 50 pounds when in reality it is not.
(D) She should fail to reject
H
0
H
0
​ . 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.
(E) She should fail to reject
H
0
H
0
​ . She could make a low power error, meaning that she rejects the null hypothesis when the null hypothesis is true.

Answer 1

Answer:

(D)

Explanation:

(D) She should fail to reject H0. 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.