Solution Found!
The life in hours of a battery is known to be
Chapter 9, Problem 45E(choose chapter or problem)
The life in hours of a battery is known to be approximately normally distributed with 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 \(\alpha = 0.05\).
(b) What is the P-value for the test in part (a)?
(c) What is the β-error for the test in part (a) if the true mean life is 42 hours?
(d) What sample size would be required to ensure that \(\beta\) does not exceed 0.10 if the true mean life is 44 hours?
(e) Explain how you could answer the question in part (a) by calculating an appropriate confidence bound on life.
Questions & Answers
QUESTION:
The life in hours of a battery is known to be approximately normally distributed with 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 \(\alpha = 0.05\).
(b) What is the P-value for the test in part (a)?
(c) What is the β-error for the test in part (a) if the true mean life is 42 hours?
(d) What sample size would be required to ensure that \(\beta\) does not exceed 0.10 if the true mean life is 44 hours?
(e) Explain how you could answer the question in part (a) by calculating an appropriate confidence bound on life.
ANSWER:Step 1 of 7
Given,
Sample size, n = 12
The sample mean,
The standard deviation,
Using the given values let’s determine the following: