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 sample of 24 small projects was randomly 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 in the table.

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 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 scatter plot based on the sample data.

What type of relationship, if any, appears to exist between the two variables?

b. Calculate the sample correlation coefficient between billed consulting hours and total project costs.

c. Conduct a hypothesis test to determine if there is a significant positive correlation between billed consulting hours and total project costs. Use a level of significance of 0.01.

Computer Software Exercises