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 117 hours. A random sample of 81 light bulbs indicated a sample mean life of 370 hours. Complete parts​ (a) through​ (d) below.a. Construct a 99​% confidence interval estimate for the population mean life of light bulbs in this shipment.The 99% confidence interval estimate is from a lower limit of 336.5 hours to an upper limit of 403.5 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 420 ​hours? Explain. Based on the sample​ data, the manufacturer [does not have / has] the right to state that the lightbulbs have a mean life of 420 hours. A mean of 420 hours is  [less than 2/more than 3]  standard errors [above/ below] the sample​ mean, so it is  [likely/ highly unlikely]  that the lightbulbs have a mean life of 420 hours.

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Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.