Question: Technology and the Internet In early 2013, Cree, Inc., introduced a new, cheap LED light that uses much less electricity and is designed to last for years. These new bulbs are replacements for traditional incandescent bulbs, and the company claims that its 60-watt warm white bulb has a brightness of 800 lumens.13 A random sample of 45 60-watt warm white bulbs was obtained and the brightness of each was carefully measured. The sample mean was = 798 lumens. Assume σ = 12.2 lumens.
a. Find a 95% confidence interval for the true mean brightness for the 60-watt warm white bulb.
b. Using your answer in part (a), is there any evidence to suggest that the mean brightness is less than 800 lumens? Justify your answer.
c. Suppose σ = 5.2. Find a 95% confidence interval for the true mean brightness for the 60-watt warm white bulb. In this case, is there any evidence to suggest that the true mean brightness is less than 800 lumens? Justify your answer.