The life in hours of a battery is known to be approximately normally distributed, with standard deviation o = 1.25 hours. A rand ample of 10 batteries has a mean life of x = 40.5 hours. a) Is there evidence to support the claim that battery life exceeds 40 hours? Use a = 0.050. The battery life significantly different greater than 40 hours at a = 0.050. b) What is the P-value for the test in part (a)? -value = i Round your answer to three decimal places (e.g. 98.765). c) What is the 6-error for the test in part (a) if the true mean life is 42 hours?
The life in hours of a battery is known to be approximately normally distributed, with standard deviation o = 1.25 hours. A rand ample of 10 batteries has a mean life of x = 40.5 hours. a) Is there evidence to support the claim that battery life exceeds 40 hours? Use a = 0.050. The battery life significantly different greater than 40 hours at a = 0.050. b) What is the P-value for the test in part (a)? -value = i Round your answer to three decimal places (e.g. 98.765). c) What is the 6-error for the test in part (a) if the true mean life is 42 hours?
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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](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F453530fe-df7b-40e0-87f7-364c227f8f51%2F5ca7608f-e6b7-4679-a5b2-1e56aa69b2d8%2Feu68dh9_processed.png&w=3840&q=75)
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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