
MATLAB: An Introduction with Applications
6th Edition
ISBN: 9781119256830
Author: Amos Gilat
Publisher: John Wiley & Sons Inc
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![**Battery Life Statistical Analysis**
The life in hours of a battery is known to be approximately normally distributed, with a standard deviation \(\sigma = 1.25\) hours. A random sample of 10 batteries has a mean life of \(\bar{x} = 40.5\) hours.
**(a)** Is there evidence to support the claim that battery life exceeds 40 hours? Use \(\alpha = 0.050\).
- The battery life is significantly different greater than 40 hours at \(\alpha = 0.050\).
**(b)** What is the *P-value* for the test in part (a)?
- *P-value* = [Input Box]
- Round your answer to three decimal places (e.g. 98.765).
**(c)** What is the *β-error* for the test in part (a) if the true mean life is 42 hours?
- \(\beta =\) [Input Box]
- Round your answer to five decimal places (e.g. 98.76543).
**(d)** What sample size would be required to ensure that \(\beta\) does not exceed 0.1 if the true mean life is 44 hours?
- [Input Box] batteries](https://content.bartleby.com/qna-images/question/453530fe-df7b-40e0-87f7-364c227f8f51/5ca7608f-e6b7-4679-a5b2-1e56aa69b2d8/eu68dh9_thumbnail.png)
Transcribed Image Text:**Battery Life Statistical Analysis**
The life in hours of a battery is known to be approximately normally distributed, with a standard deviation \(\sigma = 1.25\) hours. A random sample of 10 batteries has a mean life of \(\bar{x} = 40.5\) hours.
**(a)** Is there evidence to support the claim that battery life exceeds 40 hours? Use \(\alpha = 0.050\).
- The battery life is significantly different greater than 40 hours at \(\alpha = 0.050\).
**(b)** What is the *P-value* for the test in part (a)?
- *P-value* = [Input Box]
- Round your answer to three decimal places (e.g. 98.765).
**(c)** What is the *β-error* for the test in part (a) if the true mean life is 42 hours?
- \(\beta =\) [Input Box]
- Round your answer to five decimal places (e.g. 98.76543).
**(d)** What sample size would be required to ensure that \(\beta\) does not exceed 0.1 if the true mean life is 44 hours?
- [Input Box] batteries
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