A sample of 93 coils of sheet steel showed that the average length was 101.37 meters, with a standard deviation of 2.67 meters.
a. Interpret the standard deviation in words; in particular, what is it measuring the variability of?
b. Find the standard error. Interpret this number in words and distinguish it from the standard deviation you explained in part a.
c. Find the two-sided 95% confidence interval for the mean length of coils in the larger population. Write a brief paragraph explaining its meaning.
d. Find the two-sided 95% prediction interval for the length of the next coil to be produced. Write a brief paragraph explaining its meaning and distinguish this prediction interval from the confidence interval you found for part c. In particular, why is the prediction interval so much wider than the confidence interval?
e. Your integrity requires that you guarantee coils to be at least a certain length. Does this information make it appropriate for you to compute one-sided intervals? Why or why not?
f. Find the appropriate one-sided 99% confidence interval and explain its meaning.
g. Find the appropriate one-sided 99% prediction interval and explain its meaning.