MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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![A researcher studying stress is interested in the blood pressure measurements of chief executive officers (CEOs) of major corporations. He has good reason to believe that the mean systolic blood pressure, \(\mu\), of CEOs of major corporations is more than 132 mm Hg, which is the value reported in a possibly outdated journal article. He plans to perform a statistical test. He measures the systolic blood pressures of a random sample of CEOs of major corporations and finds the mean of the sample to be 142 mm Hg and the standard deviation of the sample to be 18 mm Hg.
Based on this information, complete the parts below.
(a) What are the null hypothesis \(H_0\) and the alternative hypothesis \(H_1\) that should be used for the test?
\[ H_0: \mu = 132 \]
\[ H_1: \mu > 132 \]
(b) Suppose that the researcher decides not to reject the null hypothesis. What sort of error might he be making?
(Choose one)
(c) Suppose the true mean systolic blood pressure of CEOs of major corporations is 146 mm Hg. Fill in the blanks to describe a Type II error.
A Type II error would be (Choose one) the hypothesis that \(\mu\) is (Choose one) (Choose one) when, in fact, \(\mu\) is (Choose one).
Terms and Symbols:
- \(\mu\): Population mean
- \(\bar{x}\): Sample mean
Functionality icons:
- Choices for selecting hypothesis symbols and conditions.
Note: The details in the shaded boxes require selection for completing the proper statistical analysis.](https://content.bartleby.com/qna-images/question/ab310076-c445-4f02-aa72-05faca788dac/02a59af0-50bc-49b3-8cd1-6145bb18cf2d/l38xpl8_processed.jpeg)
Transcribed Image Text:A researcher studying stress is interested in the blood pressure measurements of chief executive officers (CEOs) of major corporations. He has good reason to believe that the mean systolic blood pressure, \(\mu\), of CEOs of major corporations is more than 132 mm Hg, which is the value reported in a possibly outdated journal article. He plans to perform a statistical test. He measures the systolic blood pressures of a random sample of CEOs of major corporations and finds the mean of the sample to be 142 mm Hg and the standard deviation of the sample to be 18 mm Hg.
Based on this information, complete the parts below.
(a) What are the null hypothesis \(H_0\) and the alternative hypothesis \(H_1\) that should be used for the test?
\[ H_0: \mu = 132 \]
\[ H_1: \mu > 132 \]
(b) Suppose that the researcher decides not to reject the null hypothesis. What sort of error might he be making?
(Choose one)
(c) Suppose the true mean systolic blood pressure of CEOs of major corporations is 146 mm Hg. Fill in the blanks to describe a Type II error.
A Type II error would be (Choose one) the hypothesis that \(\mu\) is (Choose one) (Choose one) when, in fact, \(\mu\) is (Choose one).
Terms and Symbols:
- \(\mu\): Population mean
- \(\bar{x}\): Sample mean
Functionality icons:
- Choices for selecting hypothesis symbols and conditions.
Note: The details in the shaded boxes require selection for completing the proper statistical analysis.
Expert Solution
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Step 1
From the given information we have
The null and alternative hypothesis are
H0 : µ = 132
H1: µ > 132
Step by stepSolved in 2 steps
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