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.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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