An engineering firm is interested in investigating whether the variability in the cost of small projects

(defined as projects under $10 million) can be accounted for, in part, by differences in the number of direct engineering consulting hours billed. A random sample of 24 small projects was selected from small projects performed over the past two years. The number of engineering consulting hours billed for each project, along with the project’s cost, was recorded.

The results are shown here:

Project Billed Consulting Hours Total Project Cost 1 3,932 $4,323,826 2 3,097 $3,750,964 3 2,972 $3,579,570 4 3,994 $5,053,149 5 4,906 $5,528,308 6 5,147 $5,631,967 7 4,003 $5,257,756 8 4,279 $5,681,909 9 3,158 $4,133,012 10 4,123 $4,596,329 11 2,566 $3,344,851 12 3,253 $3,868,200 13 3,888 $4,865,998 Project Billed Consulting Hours Total Project Cost 14 3,177 $4,042,509 15 3,938 $5,067,679 16 3,135 $4,111,731 17 5,142 $6,554,583 18 5,091 $6,042,445 19 4,301 $5,192,769 20 2,914 $3,581,835 21 3,890 $4,745,269 22 2,869 $3,353,559 23 3,683 $5,169,469 24 4,217 $5,147,689

a. Develop a simple linear regression model to explain the variation in total project cost based on the number of billed consulting hours.

b. Construct and interpret a 95% confidence interval estimate for the regression slope coefficient.

c. Provide a 95% confidence interval for the average value of y when xp = 3,500.

d. Provide a 95% prediction interval for the total project cost for the a particular project with 3,500 billed consulting hours.