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.