The Energy Star rating system is an energy efficiency program run by the U.S. Environmental Protection Agency (EPA). Energy Star certified appliances, such as televisions and refrigerators, are rated in regard to their average energy consumption per year. A certain brand of Energy Star certified refrigerator is stated to have a mean yearly electricity cost of $84. A consumer advocacy organization believes that this claim is wrong, that the energy consumption of this particular refrigerator is different than $84 per year. The group collected a random sample of 16 refrigerators of the model in question and had each lab-tested for electricity consumption. The yearly energy consumption of each is given below. 83.48 83.1 83.72 84.45 83.54 83.25 84.43 84.93 84.11 84.11 83.71 83.97 84.88 84.31 83.77 84.66 Using a significance level of 20%, test the hypothesis that the average yearly electricity consumption of the refrigerator in question is different than $84 per year. Assume that the distribution of all electricity costs of this model of refrigerator is approximately normally distributed. Use the p-value method. State the null and alternative hypothesis for this test. Ho: P = 84 H₁:84 Determine if this test is left-tailed, right-tailed, or two-tailed. Oleft-tailed

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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Transcribed Image Text:### Understanding Hypothesis Testing for Energy Consumption of Refrigerators #### Introduction to the Energy Star Rating System The Energy Star rating system is an energy efficiency program run by the U.S. Environmental Protection Agency (EPA). Energy Star certified appliances, including televisions and refrigerators, are evaluated based on their average energy consumption per year. #### Case Study: Energy Consumption of a Specific Refrigerator Model A certain brand of Energy Star certified refrigerator is alleged to have a mean yearly electricity cost of $84. However, a consumer advocacy organization suspects that this claim may be inaccurate, asserting that the energy consumption of this refrigerator is different from $84 per year. To investigate this claim, the organization conducted a study by collecting a random sample of 16 refrigerators of the model in question and testing each one for electricity consumption. The yearly energy consumption of each refrigerator in the sample is as follows: | 83.48 | 83.72 | 84.45 | 83.54 | 83.25 | 84.43 | 84.93 | 84.11 | | --- | --- | --- | --- | --- | --- | --- | --- | | 83.1 | 84.11 | 83.71 | 83.97 | 84.88 | 84.31 | 83.77 | 84.66 | #### Hypothesis Testing Using a significance level of 20%, test the hypothesis that the average yearly electricity consumption of the refrigerator in question is different from $84 per year. Assume that the distribution of all electricity costs of this model of refrigerator is approximately normally distributed. Use the p-value method for this hypothesis test. ##### Stating the Hypotheses The hypotheses for this test are: Null Hypothesis (H₀): μ = 84 (The mean yearly electricity cost is $84) Alternative Hypothesis (H₁): μ ≠ 84 (The mean yearly electricity cost is not $84) ##### Determine the Type of Test Determine if this test is left-tailed, right-tailed, or two-tailed: - left-tailed - right-tailed - **two-tailed** (since we are testing for a difference, not directionality) Consider the provided data and use statistical methods to compute the relevant p-value. Based on this p-value and the given significance level, draw a conclusion about the validity of the consumer advocacy organization's claim.