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The quality control manager at a light bulb factory needs to estimate the mean life of...

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 91 hours. A random sample of 49 light bulbs indicated a sample mean life of 290 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 [ ] hours to an upper limit of [ ] 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 340 hours? Explain.

Based on the sample​ data, the manufacturer ▼ [has, does not have] the right to state that the lightbulbs have a mean life of 340 hours. A mean of 340 hours is ▼ [more than 3, less than 2, standard errors] ▼ [above, below] the sample mean, so it is ▼[ highly unlikely, likely] that the lightbulbs have a mean life of 340 hours.

C. Must you assume that the population light bulb life is normally​ distributed? Explain.

a. ​Yes, the sample size is not large enough for the sampling distribution of the mean to be approximately normal by the Central Limit Theorem.

b.​No, since σ is​ known, the sampling distribution of the mean does not need to be approximately normally distributed.

c.​No, since σ is known and the sample size is large​ enough, the sampling distribution of the mean is approximately normal by the Central Limit Theorem.

d.​Yes, the sample size is too large for the sampling distribution of the mean to be approximately normal by the Central Limit Theorem.

D. Suppose the standard deviation changes to 70 hours. What are your answers in​ (a) and​ (b)?

The 99​% confidence interval estimate would be from a lower limit of [ ] hours to an upper limit of [ ] hours.

​(Round to one decimal place as​ needed.)

Based on the sample data and a standard deviation of 70 ​hours, the manufacturer ▼[does not have, has]

the right to state that the lightbulbs have a mean life of 340 hours. A mean of 340 hours is ▼ [5, less than 2, standard] errors▼[below, above] the sample​ mean, so it is ▼[likely, highly unlikely] that the lightbulbs have a mean life of 340 hours/

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