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The life in hours of a battery is known to be approximately normally distributed, with standard deviation o = 1.25 hours. A random sample of 10 batteries has a mean life of = 40.5 hours. (a) Is there evidence to support the claim that battery life exceeds 40 hours? Use α = 0.035. The battery life is not significantly different greater than 40 hours at a = 0.035. (b) What is the P-value for the test in part (a)? P-value = i Round your answer to three decimal places (e.g. 98.765). (c) What is the B-error for the test in part (a) if the true mean life is 42 hours? B = Round your answer to five decimal places (e.g. 98.76543). (d) What sample size would be required to ensure that 3 does not exceed 0.2 if the true mean life is 44 hours? i batteries

The life in hours of a battery is known to be approximately normally distributed, with standard deviation o = 1.25 hours. A random sample of 10 batteries has a mean life of = 40.5 hours. (a) Is there evidence to support the claim that battery life exceeds 40 hours? Use α = 0.035. The battery life is not significantly different greater than 40 hours at a = 0.035. (b) What is the P-value for the test in part (a)? P-value = i Round your answer to three decimal places (e.g. 98.765). (c) What is the B-error for the test in part (a) if the true mean life is 42 hours? B = Round your answer to five decimal places (e.g. 98.76543). (d) What sample size would be required to ensure that 3 does not exceed 0.2 if the true mean life is 44 hours? i batteries

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter13: Probability And Calculus
Section13.2: Expected Value And Variance Of Continuous Random Variables
Problem 10E
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The life in hours of a battery is known to be approximately normally distributed, with standard deviation o = 1.25 hours. A random sample of 10 batteries has a mean life of = 40.5 hours. (a) Is there evidence to support the claim that battery life exceeds 40 hours? Use α = 0.035. The battery life is not significantly different greater than 40 hours at a = 0.035. (b) What is the P-value for the test in part (a)? P-value = i Round your answer to three decimal places (e.g. 98.765). (c) What is the ß-error for the test in part (a) if the true mean life is 42 hours? B = Round your answer to five decimal places (e.g. 98.76543). (d) What sample size would be required to ensure that 3 does not exceed 0.2 if the true mean life is 44 hours? batteries
Transcribed Image Text:The life in hours of a battery is known to be approximately normally distributed, with standard deviation o = 1.25 hours. A random sample of 10 batteries has a mean life of = 40.5 hours. (a) Is there evidence to support the claim that battery life exceeds 40 hours? Use α = 0.035. The battery life is not significantly different greater than 40 hours at a = 0.035. (b) What is the P-value for the test in part (a)? P-value = i Round your answer to three decimal places (e.g. 98.765). (c) What is the ß-error for the test in part (a) if the true mean life is 42 hours? B = Round your answer to five decimal places (e.g. 98.76543). (d) What sample size would be required to ensure that 3 does not exceed 0.2 if the true mean life is 44 hours? batteries
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