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d. Suppose the standard deviation changes to 108 hours. What are your answers in (a) and (b)? The 95% confidence interval estimate would be from a lower limit of (Round to one decimal place as needed.) hours to an upper limit of hours.

d. Suppose the standard deviation changes to 108 hours. What are your answers in (a) and (b)? The 95% confidence interval estimate would be from a lower limit of (Round to one decimal place as needed.) hours to an upper limit of hours.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Answer D

The quality control manager at a light bulb factory needs to estimate the mean life of a large shipment of light bulbs. The standard deviation is 126 hours. A random sample of 81 light bulbs indicated a sample mean life of hours. Complete parts (a) through (d) below. a. Construct a 95% confidence interval estimate for the population mean life of light bulbs in this shipment. The 95% confidence interval estimate is from a lower limit of 362.6 hours to an upper limit of 417.4 hours. (Round to one decimal place as needed.) b. Do you think that the manufacturer has the right to state that the lightbulbs have a mean life of 440 hours? Explain. Based on the sample data, the manufacturer does not have the right to state that the lightbulbs have a mean life of 440 hours. A mean of 440 hours is more than 3 standard errors above the sample mean, so it is highly unlikely that the lightbulbs have a mean life of 440 hours. c. Must you assume that the population light bulb life is normally distributed? Explain. C O A. Yes, the sample size is too large for the sampling distribution of the mean to be approximately normal by the Central Limit Theorem. O B. Yes, the sample size is not large enough for the sampling distribution of the mean to be approximately normal by the Central Limit Theorem. C. No, since o is known and the sample size is large enough, the sampling distribution of the mean is approximately normal by the Central Limit Theorem. O D. No, since o is known, the sampling distribution of the mean does not need to be approximately normally distributed. d. Suppose the standard deviation changes to 108 hours. What are your answers in (a) and (b)? The 95% confidence interval estimate would be from a lower limit of hours to an upper limit of (Round to one decimal place as needed.) hours.
Transcribed Image Text:The quality control manager at a light bulb factory needs to estimate the mean life of a large shipment of light bulbs. The standard deviation is 126 hours. A random sample of 81 light bulbs indicated a sample mean life of hours. Complete parts (a) through (d) below. a. Construct a 95% confidence interval estimate for the population mean life of light bulbs in this shipment. The 95% confidence interval estimate is from a lower limit of 362.6 hours to an upper limit of 417.4 hours. (Round to one decimal place as needed.) b. Do you think that the manufacturer has the right to state that the lightbulbs have a mean life of 440 hours? Explain. Based on the sample data, the manufacturer does not have the right to state that the lightbulbs have a mean life of 440 hours. A mean of 440 hours is more than 3 standard errors above the sample mean, so it is highly unlikely that the lightbulbs have a mean life of 440 hours. c. Must you assume that the population light bulb life is normally distributed? Explain. C O A. Yes, the sample size is too large for the sampling distribution of the mean to be approximately normal by the Central Limit Theorem. O B. Yes, the sample size is not large enough for the sampling distribution of the mean to be approximately normal by the Central Limit Theorem. C. No, since o is known and the sample size is large enough, the sampling distribution of the mean is approximately normal by the Central Limit Theorem. O D. No, since o is known, the sampling distribution of the mean does not need to be approximately normally distributed. d. Suppose the standard deviation changes to 108 hours. What are your answers in (a) and (b)? The 95% confidence interval estimate would be from a lower limit of hours to an upper limit of (Round to one decimal place as needed.) hours.
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The sample size is 81, the sample mean life is 390 hours and the standard deviation is 108 hours.

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