Question

3. The operations manager at a compact fluorescent line bulb (CFL) factory needs to estimate the mean life of a large shipment of CFLs. The manufacturer’s specifications are that the standard deviation is 1,000 hours. A random sample of 64 CFLs indicated a sample mean life of 7,500 hours.

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

b. Do you think that the manufacturer has the right to state that the compact fluorescent light bulbs have a mean life of 8,000 hours? Explain.

c. Must you assume that the population compact fluorescent light bulb life is normally distributed? Explain.

d. Suppose that the standard deviation changes to 800 hours. What are your answers in (a) and (b)?

Answer 1

a) At 95% confidence interval the critical value is z_0.025 = 1.96

The 95% confidence interval for population mean is

+/- z_0.025 *

= 7500 +/- 1.96 * 1000/

= 7500 +/- 245

= 7255, 7745

b) Since 8000 does not fall in the confidence interval, so the manufacturer has not right to state the compact fluorescent light bulbs have a mean life of 8000 hours.

c) Since the sample size is large (n > 30), so according to the Central Limit Theorem the sampling distribution of the sample mean is approximately normally distributed.

So there is no need to assume that the population compact fluorescent light bulb life is normally distributed.

d)

The 95% confidence interval for population mean is

+/- z_0.025 *

= 7500 +/- 1.96 * 800/

= 7500 +/- 196

= 7304, 7696

Since 8000 does not fall in the confidence interval, so the manufacturer has not right to state the compact fluorescent light bulbs have a mean life of 8000 hours.