The quality control manager at a light bulb factory needs to

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 78 hours. A random sample of 36 light bulbs indicated a sample mean life of 290 hours. Complete parts (a) through (d) below.

Construct a 95% confidence interval estimate for the population mean life of light bulbs in this shipment.

The 95% confidence interval estimate is from a lower limit of________ hours to an upper limit of _________ hours. (Round to one decimal place as needed)

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 (does not have) or (has ) the right to state that the lightbulbs have a mean life of 340 hours? A mean of 340 hours is (more than 3) or (less than 2) standard errors (below) or (above) the sample mean, so it is (likely) or (highly unlikely) the lightbulbs have a mean life of 340 hours.

C.)Must you assume that the population light bulb life is normal distributed? Explain.

(Choose Best Answer Below)

a.)No, since ? is known, the sampling distribution of the mean does not need to be approximately normally distributed.

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

c.) No, since ? 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 not large enough for the sampling distribution of the mean to be approximately normal by the Central Limit Theorem.

D.) Suppose the standard deviation changes to 63 hours. What are your answers in (a) and (b)?

Solution

The 95% confidence interval estimate is from a lower limit of 264.5 hours to an upper limit of 315.5 hours.

Do you think that the manufacturer has the right to state that the lightbulbs have a mean life of 340 hours? Explain.

No. Because at 95% 340 is is not included in the 95% confidence interval

Based on the sample data, the manufacturer (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) standard errors (above) the sample mean, so it is (highly unlikely) the lightbulbs have a mean life of 340 hours.

C.)Must you assume that the population light bulb life is normal distributed? Explain.

(Choose Best Answer Below)

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

D.) Suppose the standard deviation changes to 63 hours. What are your answers in (a) and (b)?

The 95% confidence interval estimate is from a lower limit of 269.4 hours to an upper limit of 310.6 hours.

Do you think that the manufacturer has the right to state that the lightbulbs have a mean life of 340 hours? Explain.

No. Because at 95% 340 is is not included in the 95% confidence interval

Based on the sample data, the manufacturer (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) standard errors (above) the sample mean, so it is (highly unlikely) the lightbulbs have a mean life of 340 hours.