Question

Oilfield pipes are internally coated in order to prevent corrosion Researchers at a university investigated the influence that coating may have on the surfaceroughness of oil field pipes. A scanning probe instrument was used to measure the surface roughness of each section in a sample of 12 sections of coatedinterior pipe. The data (in micrometers) are shown in the table to the right. A Minitab analysis of the data is given below. Complete parts a and b.One-Sample T: ROUGHVariableMeanStDev SE Mean 95%CIROUGH 12 1.86417 0.48033 0.13886 (1.55898, 2.16935)1.682251.342.182.392.17N2.511.162.061.991.481.16a. Locate a 95% confidence interval for the mean surface roughness of coated interior pipe on the accompanying Minitab printout.C (Type integers or a decimals.)b. Would you expect the average surface roughness to be as high as 2.5 micrometors? Explain.O A. Yes, because we can be 95% confident that the mean surface roughness lies between the lower and upper bounds of the interval, and 2.5 lies within the interval,OB. Yes, because we can be 95% confident that the mean surface roughness lies outside the lower and upper bounds of the interval, and 25 lies within the interval.OC. Yes, because we can be 95% confident that the mean surface roughness lios outside the lower and upper bounds of the interval, and 2.5 lies outside the intervalOD. No, becauso we can be 95% confident that the mean surface roughness lies between the lower and upper bounds of the interval, and 2.5 lios outside the interval.

Answer 1

a.

The minitab analysis shows the summary statistics of the sample of sections of coated interior pipes.

The first column "variable" indicates what is the characteristic in the study, in this case, the variable is X: surface roughness of oil field pipes. Named: "Rough"

The second column indicates the size of the sample taken, N=12

The third column shows you the value of the calculated sample mean, Mean= 1.86417

The fourth column shows the calculated value of the sample standard deviation (S), StDev=0.48033

The fifth column shows the standard deviation of the mean, SE Mean=0.13866

The sixth column shows the 95% confidence interval for the population mean, 95% CI (1.55898,2.16935)

The confidence interval for the mean surface roughness of coated interior pipe is (1.55898,2.16935)

b.

The confidence interval indicates that with a 95% of confidence, the true value of the mean surface roughness of coated interior pipe is found between 1.55898 and 2.16935 micrometers.

A roughness of 2.5 micrometers is higher than the upper bound of the calculated confidence interval. Since this value is not included in the confidence interval, you cannot expect the average surface roughness to be as high as 2.5 micrometers.

The correct option is D. No, because we can be 95% confident that the mean surface roughness lies between the lower and upper bounds of the interval and 2.5 lies outside the interval.