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.

Question
Asked Oct 18, 2019
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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
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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Expert Answer

Step 1

From the given information,

Sample mean life of bulbs = 370 hrs.

Populat

From the given information,

Sample mean life of bulbs = 370 hrs.

Population standard deviation(σ) = 117 hrs.

Sample size = 81,

ion standard deviation(σ) = 117 hrs.

Sample size = 81,

Step 2

a)

A 99% confidence interval estimate for the population mean life of light bulbs is given as:

n
117
370 2.57x
/81
(336.59,403.41)
X
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n 117 370 2.57x /81 (336.59,403.41) X

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Step 3

Therefore, the 99% confidence interval of the me...

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Hypothesis Testing

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