Please answer D # Hypothesis Testing and Error Analysis in Quality Control## Scenario:A can of soda is labeled as containing 14 fluid ounces. The quality control manager wants to verify that the filling machine is not over-filling the cans. Complete parts (a) through (d) below.### (a) Determine the null and alternative hypotheses- Null hypothesis ($H_0$): $\mu = 14$- Alternative hypothesis ($H_a$): $\mu > 14$(Type integers or decimals. Do not round.)### (b) Sample Evidence and ConclusionThe quality control manager obtains a sample of 84 cans and measures the contents. The sample evidence leads the manager to reject the null hypothesis. Write a conclusion for this hypothesis test.- **Conclusion:** There is sufficient evidence to conclude that the machine is out of calibration.### (c) Error Type AnalysisSuppose, in fact, the machine is not out of calibration. Has a Type I or Type II error been made?- **Error Type:** A Type I error- **Explanation:** A Type I error has been made since the sample evidence led the quality-control manager to reject the null hypothesis when the null hypothesis is true.### (d) Management Decision and Significance LevelManagement has informed the quality control department that it does not want to shut down the filling machine unless the evidence is overwhelming that the machine is out of calibration. What level of significance should the quality control manager use? Explain.- **Recommended Significance Level:** 0.01- **Explanation:** The level of significance should be 0.01 because this makes the probability of a Type I error low.### Interactive Elements:- **Significance Level Selection:** Options include 0.01, 0.1, and 0.05. The checkbox allows the user to select their answer(s) and then click "Check Answer."End of Document.

D) Type I Error: The type I error occurs if “rejecting the null hypothesis if the null hypothesis…

a) Determine the null and alternative hypotheses that would be used to determine if the filling machine is calibrated correctly. Ho: H 14 %3D H: H 14 <> (Type integers or decimals. Do not round.) (b) The quality control manager obtains a sample of 84 cans and measures the contents. The sample evidence leads the manager to reject the null hypothesis. Write a conclusion for this hypothesis test. There is sufficient evidence to conclude that the machine is out of calibration. (c) Suppose, in fact, the machine is not out of calibration. Has a Type I or Type II error been made? A Type I error has been made since the sample evidence led the quality-control manager to reject the null hypothesis, when the null hypothesis is true. (d) Management has informed the quality control department that it does not want to shut down the filling machine unless the evidence is overwhelming that the machine is out of calibration. What level of si recommend the quality control manager to use? Explain.

a) Determine the null and alternative hypotheses that would be used to determine if the filling machine is calibrated correctly. Ho: H 14 %3D H: H 14 <> (Type integers or decimals. Do not round.) (b) The quality control manager obtains a sample of 84 cans and measures the contents. The sample evidence leads the manager to reject the null hypothesis. Write a conclusion for this hypothesis test. There is sufficient evidence to conclude that the machine is out of calibration. (c) Suppose, in fact, the machine is not out of calibration. Has a Type I or Type II error been made? A Type I error has been made since the sample evidence led the quality-control manager to reject the null hypothesis, when the null hypothesis is true. (d) Management has informed the quality control department that it does not want to shut down the filling machine unless the evidence is overwhelming that the machine is out of calibration. What level of si recommend the quality control manager to use? Explain.

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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Question

Please answer D

# Hypothesis Testing and Error Analysis in Quality Control

## Scenario:

A can of soda is labeled as containing 14 fluid ounces. The quality control manager wants to verify that the filling machine is not over-filling the cans. Complete parts (a) through (d) below.

### (a) Determine the null and alternative hypotheses

- Null hypothesis ($H_0$): $\mu = 14$
- Alternative hypothesis ($H_a$): $\mu > 14$

(Type integers or decimals. Do not round.)

### (b) Sample Evidence and Conclusion

The quality control manager obtains a sample of 84 cans and measures the contents. The sample evidence leads the manager to reject the null hypothesis. Write a conclusion for this hypothesis test.

- **Conclusion:** There is sufficient evidence to conclude that the machine is out of calibration.

### (c) Error Type Analysis

Suppose, in fact, the machine is not out of calibration. Has a Type I or Type II error been made?

- **Error Type:** A Type I error

- **Explanation:** A Type I error has been made since the sample evidence led the quality-control manager to reject the null hypothesis when the null hypothesis is true.

### (d) Management Decision and Significance Level

Management has informed the quality control department that it does not want to shut down the filling machine unless the evidence is overwhelming that the machine is out of calibration. What level of significance should the quality control manager use? Explain.

- **Recommended Significance Level:** 0.01

- **Explanation:** The level of significance should be 0.01 because this makes the probability of a Type I error low.

### Interactive Elements:

- **Significance Level Selection:** Options include 0.01, 0.1, and 0.05. The checkbox allows the user to select their answer(s) and then click "Check Answer."

End of Document.

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