### Hypothesis Testing in Quality Control**Scenario:**A company that manufactures hearing aids aims to have no more than 10 defective hearing aids per shipment. Recently, a company executive sampled 32 shipments and discovered an average of 8.5 defective hearing aids per shipment, with a standard deviation of 4.2. She asserts that this indicates the company is meeting its goal. To test her claim, we will employ a significance level (alpha) of 0.05.**Possible Outcomes and Their Interpretations:**1. **Reject the null hypothesis with a p-value of greater than 0.05**2. **Fail to reject the null hypothesis with a p-value of greater than 0.05**3. **Reject the null hypothesis with a p-value of less than 0.05**4. **Fail to reject the null hypothesis with a p-value of less than 0.05**#### Detailed Explanation of Options:- **Reject the null hypothesis with a p-value of greater than 0.05:** This outcome suggests that the p-value (the probability of obtaining results at least as extreme as the ones observed, given that the null hypothesis is true) is greater than the significance level. If this is the case, it indicates weak evidence against the null hypothesis, and therefore it is not rejected.- **Fail to reject the null hypothesis with a p-value of greater than 0.05:** This scenario implies that the p-value is greater than alpha = 0.05, meaning there is insufficient evidence to reject the null hypothesis. This supports the claim that the company's hearing aid defect rate meets the specified goal.- **Reject the null hypothesis with a p-value of less than 0.05:** If the p-value is less than the chosen alpha of 0.05, we reject the null hypothesis. This would suggest that the true defect rate is significantly different from the goal stated (less than 10 defects per shipment).- **Fail to reject the null hypothesis with a p-value of less than 0.05:** This outcome is contradictory because failing to reject the null hypothesis typically occurs when the p-value is greater than the significance level. Therefore, this option would be inconsistent and likely indicates a misunderstanding.Understanding p-values and hypothesis testing is essential for quality control and business decision-making. The correct analysis of the situation should lead to either rejection or failure to reject the null hypothesis, guiding the

Given:n = 32x̄ = 8.5s = 4.2α = 0.05

Answered: A company who manufactures hearing aids…

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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