# Question

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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