solution

Structurally deficient highway bridges. Refer to Exercise 1.30 (p. 52) and the data on structurally deficient highway bridges compiled by the Federal Highway Administration (FHWA) into the National Bridge Inventory (NBI). For each state, the NBI lists the number of structurally deficient bridges and the total area (thousands of square feet) of the deficient bridges. The data for the 50 states (plus the District of Columbia and Puerto Rico) are saved in the file. (The first five and last five observations are listed in the table in the next column.) For future planning and budgeting, the FHWA wants to estimate the total area of structurally deficient bridges in a state based on the number of deficient bridges.

a. Write the equation of a straight-line model relating total area (y) to number of structurally deficient bridges (x).

b. The model, part a, was fit to the data using Minitab, as shown below. Find the least squares prediction equation on the printout.

c. List the assumptions required for the regression analysis.

d. Locate the estimated standard error of the regression model, s, on the printout.

e. Use the value of s to find a range where most (about 95%) of the errors of prediction will fall.

Exercise 1.30

Structurally deficient highway bridges. Refer to Exercise 1.29. The NBI data were analyzed and the results made available at the FHWA Web site (www.fhwa.dot.gov). Using the FHWA inspection ratings, each of the 608,272 highway bridges in the United States was categorized as structurally deficient, functionally obsolete, or safe. About 13.5% of the bridges were found to be structurally deficient, while 3.5% were functionally obsolete.

a. What is the variable of interest to the researchers?

b. Is the variable of part a quantitative or qualitative?

c. Is the data set analyzed a population or a sample? Explain.

d. How did the NBI obtain the data for the study?

Exercise 1.29

Inspection of highway bridges. All highway bridges in the United States are inspected periodically for structural deficiency by the Federal Highway Administration (FHWA). Data from the FHWA inspections are compiled into the National Bridge Inventory (NBI). Several of the nearly 100 variables maintained by the NBI are listed below. Classify each variable as quantitative or qualitative.

a. Length of maximum span (feet)
b. Number of vehicle lanes
c. Toll bridge (yes or no)
d. Average daily traffic
e. Condition of deck (good, fair, or poor)
f. Bypass or detour length (miles)
g. Route type (interstate, U.S., state, county, or city)