Applied Statistics and Probability for Engineers

10-38. A computer scientist is investigating the usefulness

of two different design languages in improving programming

tasks. Twelve expert programmers, familiar with both lan-

guages, are asked to code a standard function in both lan-

guages, and the time (in minutes) is recorded. The data follow:

354 CHAPTER 10 STATISTICAL INFERENCE FOR TWO SAMPLES

Car Brand 1 Brand 2

1 36,925 34,318

2 45,300 42,280

3 36,240 35,500

4 32,100 31,950

5 37,210 38,015

6 48,360 47,800

7 38,200 37,810

8 33,500 33,215

Time

Design Design

Language Language

Programmer 1 2

11718

21614

32119

41411

51823

62421

71610

81413

92119

10 23 24

11 13 15

12 18 20

Blood Cholesterol Level

Subject Before After

1 265 229

2 240 231

3 258 227

4 295 240

5 251 238

6 245 241

7 287 234

8 314 256

9 260 247

10 279 239

11 283 246

12 240 218

13 238 219

14 225 226

15 247 233

(a) Find a 95% confidence interval on the difference in mean

coding times. Is there any indication that one design lan-

guage is preferable?

(b) Is the assumption that the difference in coding time is nor-

mally distributed reasonable? Show evidence to support

your answer.

10-40. An article in the Journal of Aircraft(Vol. 23, 1986,

pp. 859–864) describes a new equivalent plate analysis

method formulation that is capable of modeling aircraft

structures such as cranked wing boxes and that produces

results similar to the more computationally intensive finite

element analysis method. Natural vibration frequencies for

the cranked wing box structure are calculated using both

methods, and results for the first seven natural frequencies

follow:

Finite Equivalent

Element Plate,

Freq. Cycle/s Cycle/s

1 14.58 14.76

2 48.52 49.10

3 97.22 99.99

4 113.99 117.53

5 174.73 181.22

6 212.72 220.14

7 277.38 294.80

10-36. Reconsider the parking data in Example 10-10.

Investigate the assumption that the differences in parking

times are normally distributed.

10-37. The manager of a fleet of automobiles is testing two

brands of radial tires and assigns one tire of each brand at ran-

dom to the two rear wheels of eight cars and runs the cars un-

til the tires wear out. The data (in kilometers) follow. Find a

99% confidence interval on the difference in mean life. Which

brand would you prefer, based on this calculation?

10-39. Fifteen adult males between the ages of 35 and 50

participated in a study to evaluate the effect of diet and ex-

ercise on blood cholesterol levels. The total cholesterol was

measured in each subject initially and then three months af-

ter participating in an aerobic exercise program and switch-

ing to a low-fat diet. The data are shown in the accompany-

ing table. Do the data support the claim that low-fat diet and

aerobic exercise are of value in producing a mean reduction

in blood cholesterol levels? Use 0.05.

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