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 84 hours. A random sample of 49 light bulbs indicated a sample mean life of 270 hours.    Suppose the standard deviation changes to 63 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 _______ hours.   My answer for (a) is:  The 95​% confidence interval estimate is from a lower limit of 246.5 hours to an upper limit of 293.5 hours.   My answer for (b) is: Based on the sample​ data, the manufacturer does not have the right to state that the lightbulbs have a mean life of 320 hours. A mean of 320 hours is more than 4 standard errors above the sample​ mean, so it is highly unlikely that the lightbulbs have a mean life of 320 hours.

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
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Chapter1: Starting With Matlab
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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 84 hours. A random sample of 49 light bulbs indicated a sample mean life of 270 hours. 

 

Suppose the standard deviation changes to 63
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 _______ hours.
 
My answer for (a) is: 
The 95​% confidence interval estimate is from a lower limit of
246.5 hours to an upper limit of 293.5 hours.
 
My answer for (b) is:
Based on the sample​ data, the manufacturer
does not have the right to state that the lightbulbs have a mean life of
320 hours. A mean of 320 hours is more than 4 standard errors above
the sample​ mean, so it is highly unlikely that the lightbulbs have a mean life of 320 hours.
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