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The life in hours of a battery is known to be approx- imately normally distributed with standard deviation o = 1.25 hours. A random sample 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 = 0.05.

The life in hours of a battery is known to be approx- imately normally distributed with standard deviation o = 1.25 hours. A random sample 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 = 0.05.

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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+ The life in hours of a battery is known to be approx- imately normally distributed with standard deviation o = 1.25 hours. A random sample 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 = 0.05. (b) What is the P-value for the test in part (a)? (c) What is the B-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 B 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.
Transcribed Image Text:+ The life in hours of a battery is known to be approx- imately normally distributed with standard deviation o = 1.25 hours. A random sample 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 = 0.05. (b) What is the P-value for the test in part (a)? (c) What is the B-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 B 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.
a. 1.26 = z0 < za = 1.65, than we should fail to reject Ho. b. P-value=0.103835. c. B = 0.000325. d. n z 1. e. 39.85 < µ.
Transcribed Image Text:a. 1.26 = z0 < za = 1.65, than we should fail to reject Ho. b. P-value=0.103835. c. B = 0.000325. d. n z 1. e. 39.85 < µ.
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