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Perform and interpret a hypothesis test to determine whether the population propo batches is higher than 7%, at the a = 0.05 significance level. Based on this result, does be shut down and reset?

Perform and interpret a hypothesis test to determine whether the population propo batches is higher than 7%, at the a = 0.05 significance level. Based on this result, does be shut down and reset?

MATLAB: An Introduction with Applications
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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**Text for Educational Website:** 1. A plant mixes small batches of custom paint. A batch is considered a failure if it doesn’t meet specification; failed batches must be discarded. The company set the maximum acceptable failure rate at 7%. Regular tests are taken from the population of batches, to test whether the failure rate is too high. Any proportion of failed batches higher than 7% results in a temporary shut-down to reset. The plant quality control analyst took a random sample of 125 batches, and found that 17 of them didn’t meet specification (that is, they were failures). **Objective:** Perform and interpret a hypothesis test to determine whether the population proportion of failed batches is higher than 7%, at the α = 0.05 significance level. Based on this result, does the plant need to be shut down and reset?
Transcribed Image Text:**Text for Educational Website:** 1. A plant mixes small batches of custom paint. A batch is considered a failure if it doesn’t meet specification; failed batches must be discarded. The company set the maximum acceptable failure rate at 7%. Regular tests are taken from the population of batches, to test whether the failure rate is too high. Any proportion of failed batches higher than 7% results in a temporary shut-down to reset. The plant quality control analyst took a random sample of 125 batches, and found that 17 of them didn’t meet specification (that is, they were failures). **Objective:** Perform and interpret a hypothesis test to determine whether the population proportion of failed batches is higher than 7%, at the α = 0.05 significance level. Based on this result, does the plant need to be shut down and reset?
Expert Solution
Step 1

It is given that 

Favourable cases, X = 17

Sample size, n = 125

Population proportion, p = 7% = 0.07

Sample proportion, p^ = X/n

                                        = 17/125 = 0.136

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