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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