Introduction to Probability and Statistics for Engineers and Scientists

Problems 415

5. The following data indicate the gain in reading speed versus the number of weeks
   in the program of 10 students in a speed-reading program.

Speed Gain

Number of Weeks (wds/min)

221

342

8 102

11 130

452

557

9 105

785

562

790

(a) Plot a scatter diagram to see if a linear relationship is indicated.

(b) Find the least squares estimates of the regression coefficients.

(c) Estimate the expected gain of a student who plans to take the program for

7 weeks.

6. Infrared spectroscopy is often used to determine the natural rubber content of
   mixtures of natural and synthetic rubber. For mixtures of known percentages, the
   infrared spectroscopy gave the following readings:

Percentage 02040 60 80100

Reading .734 .885 1.050 1.191 1.314 1.432

If a new mixture gives an infrared spectroscopy reading of 1.15, estimate its

percentage of natural rubber.

7. The following table gives the 1996 SAT mean math and verbal scores in each
   state and the District of Columbia, along with the percentage of the states’ gradu-
   ating high school students that took the examination. Use data relating to the
   first 20 locations listed (Alabama to Maine) to develop a prediction of the mean
   student mathematics score in terms of the percentage of students that take the
   examination. Then compare your predicted values for the next 5 states (based on
   the percentage taking the exam in these states) with the actual mean math scores.