Oil field pipes are internally coated in order to prevent corrosion. Researchers at the University of Louisiana, Lafayette, investigated the influence that coating may have on the surface roughness of oil field pipes. A scanning probe instrument was used to measure the surface roughness of each in a sample of 20 sections of coated interior pipe. The data (in micrometers) is provided in the table.
1.72 2.50 2.16 2.13 1.06 2.24 2.31 2.06 1.09 1.40
2.57 2.64 1.26 2.05 1.19 2.13 1.27 1.51 2.41 1.95
a. Calculate a 99% confidence interval for the mean surface roughness of coated interior pipe.
b. Would you expect the average surface roughness of all pipes to be as high as 2.5? Explain.
c. Based on your confidence interval, is it reasonable to assume that 99% of pipes have surface roughness measurements that fall in that interval? Briefly explain your answer.
d. With a 99% probability, how large of a sample needs to be taken to provide a margin of error of .2 micrometers or less?