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? (A) She should reject H_0H0. 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_0H0. 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_0H0. 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_0H0. 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_0H0. She could make a low power error, meaning that she rejects the null hypothesis when the null hypothesis is true.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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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 H_a: \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?

(A) She should reject H_0H0. 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_0H0. 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_0H0. 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_0H0. 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_0H0. She could make a low power error, meaning that she rejects the null hypothesis when the null hypothesis is true.

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