MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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### Statistical Hypothesis Testing Example

A 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 Statistic

Kelly calculates the test statistic, which should be rounded to two decimal places.

#### (c) p-value

Using a statistical table, she finds the p-value, rounded to four decimal places.

#### (d) Decision Based on p-value

Kelly decides to "fail to reject" the null hypothesis based on the p-value.

#### (e) Conclusion

The 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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Transcribed Image Text:### Statistical Hypothesis Testing Example A 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 Statistic Kelly calculates the test statistic, which should be rounded to two decimal places. #### (c) p-value Using a statistical table, she finds the p-value, rounded to four decimal places. #### (d) Decision Based on p-value Kelly decides to "fail to reject" the null hypothesis based on the p-value. #### (e) Conclusion The 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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