### Statistical Hypothesis Testing ExampleA computer manufacturing company claims that only 7.2% of their computers are returned. Kelly suspects that the company is underreporting and believes the true proportion is higher. She decides to test this hypothesis at a significance level (\(\alpha\)) of 0.01. Kelly samples 300 computers and finds that 25 are returned. Assume a normal sampling distribution.#### (a) Null and Alternative Hypotheses- **Null Hypothesis (\(H_0\))**: \(p = 0.072\)- **Alternative Hypothesis (\(H_A\))**: \(p > 0.072\)#### (b) Test StatisticKelly calculates the test statistic, which should be rounded to two decimal places.#### (c) p-valueUsing a statistical table, she finds the p-value, rounded to four decimal places.#### (d) Decision Based on p-valueKelly decides to "fail to reject" the null hypothesis based on the p-value.#### (e) ConclusionThe data "does not provide" sufficient evidence to conclude that the true proportion of computers returned is higher than the company claims.This exercise illustrates the process of hypothesis testing in statistics, emphasizing the importance of understanding how to interpret statistical data to make informed decisions.

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Answered: A computer manufacturing company claims…

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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1. In a study of perception, 110 men are tested and 24 are found to have red/green color blindness (based on data from USA Today). Assume that this was done in a simple random manner. A 95% confidence interval estimate of the proportion of all men with red/green color blindness was found to be 0.14 to 0.30. If we learn that the actual population proportion of men with red/green colorblindness is equal to 0.12, then what can we conclude? A. The confidence interval was wrong. B. We would need to see the sample data to make any conclusions Pick either answer A or B as your answer and show your work to go with it
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A computer manufacturing company claims that only 7.2% of their computers are returned. Kelly thinks that the company is misrepresenting the true proportion of computers that are returned, and that the true proportion is higher than they claim. She wants to test this using a = 0.01. Kelly takes a sample of 255 computers and observes that 23 are returned. Assume a normal sampling distribution. (a) What are the null and alternative hypotheses? Но: р 0.072 + HA: p 0.072 + (b) What is the test statistic? (Round your answer to 2 decimal places, if needed.) (c) Using the statistical table, what is the p-value? (Round your answer to 4 decimal places, if needed.) (d) Based on the p-value, Kelly should fail to reject + the null hypothesis. (e) This data does not provide + sufficient evidence to conclude that the true proportion of computers is higher than claimed.
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