# Question: The following partial MINITAB regression output for the natural gas

The following partial MINITAB regression output for the natural gas consumption data relates to predicting the city’s natural gas consumption (in MMcF) in a week that has an average hourly temperature of 40° F and a chill index of 10.

a. Report (as shown on the computer output) a point estimate of and a 95 percent confidence interval for the mean natural gas consumption for all weeks having an average hourly temperature of 40° F and a chill index of 10.

b. Report (as shown on the computer output) a point prediction of and a 95 percent prediction interval for the natural gas consumption in a single week that has an average hourly temperature of 40° F and a chill index of 10.

c. Suppose that next week the city’s average hourly temperature will be 40° F and the city’s chill index will be 10. Also, suppose the city’s natural gas company will use the point prediction y-bar = 10.333 and order 10.333 MMcF of natural gas to be shipped to the city by a pipeline trans-mission system. The gas company will have to pay a fine to the transmission system if the city’s actual gas usage y differs from the order of 10.333 MMcF by more than 10.5 percent—that is, is outside of the range [10.333 ± .105(10.333)] [9.248, 11.418]. Discuss why the 95 percent prediction interval for y, [9.293, 11.374], says that y is likely to be inside the allowable range and thus makes the gas company 95 percent confident that it will avoid paying a fine.

d. Find 99 percent confidence and prediction intervals for the mean and actual natural gas consumption referred to in parts a and b. n = 8 and s = .367078. Optional technical note needed.

a. Report (as shown on the computer output) a point estimate of and a 95 percent confidence interval for the mean natural gas consumption for all weeks having an average hourly temperature of 40° F and a chill index of 10.

b. Report (as shown on the computer output) a point prediction of and a 95 percent prediction interval for the natural gas consumption in a single week that has an average hourly temperature of 40° F and a chill index of 10.

c. Suppose that next week the city’s average hourly temperature will be 40° F and the city’s chill index will be 10. Also, suppose the city’s natural gas company will use the point prediction y-bar = 10.333 and order 10.333 MMcF of natural gas to be shipped to the city by a pipeline trans-mission system. The gas company will have to pay a fine to the transmission system if the city’s actual gas usage y differs from the order of 10.333 MMcF by more than 10.5 percent—that is, is outside of the range [10.333 ± .105(10.333)] [9.248, 11.418]. Discuss why the 95 percent prediction interval for y, [9.293, 11.374], says that y is likely to be inside the allowable range and thus makes the gas company 95 percent confident that it will avoid paying a fine.

d. Find 99 percent confidence and prediction intervals for the mean and actual natural gas consumption referred to in parts a and b. n = 8 and s = .367078. Optional technical note needed.

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