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 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 below:
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.