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 98 hours. A random sample of 49 light bulbs indicated a sample mean life of 300 hours.
(a) Construct a 99% confidence interval estimate for the population mean life of light bulbs in this shipment.
(Ans.) The 99% confidence interval estimate is from a lower limit of 263.9 hours to an upper limit of 336.1 hours.
(b) Do you think that the manufacturer has the right to state that the lightbulbs have a mean life of 350 hours. Explain.
(Ans.) Based on the sample data, the manufacturer does not have the right to state that the lightbulbs have a mean life of 350 hours. A mean of 350 hours is more than 3 standard errors above the sample mean, so it is highly unlikely that the lightbulbs have a mean life of 350 hours.
(c) Suppose the standard deviation changes to 77 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)
a)
z value at 99% = 2.576
CI = mean +/- z *(s/sqrt(n))
= 300 +/- 2.576 *(98/sqrt(49))
= (263.9 , 336.1 )
Lower limit = 263.9
Upper limit = 336.1
b)
mean = 300 sd = 98
3 *sd = 3 * 98 = 294
350 > 294
the manufacturer does not have the right to state that the
lightbulbs have a mean life of 350 hours.
c)
sd = 77
z value at 99% = 2.576
CI = mean +/- z *(s/sqrt(n))
= 300 +/- 2.576 *(77/sqrt(49))
= (271.7 , 328.3)
Lower limit = 271.7
Upper limit = 328.3
The 99% CI is 271.7 to 328.3 hours
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