STATS Chapter 10 Four Problems - 10.10, 10.17, 10.26 and 10.46 answers

10.10 The Computer Anxiety Rating Scale (CARS) measures an individual’s level of computer anxiety, on a scale from 20 (no anxiety) to 100 (highest level of anxiety). Researchers at Miami University administered CARS to 172 business students. One of the objectives of the study was to determine whether there is a difference in the level of computer anxiety experienced by female and male business students. They found the following:
Males Females
¯X 40.26 36.85
S 13.35 9.42
n 100 72
a. At the 0.05 level of significance, is there evidence of a difference in the mean computer anxiety experienced by female and male business students?
b. Determine the p-value and interpret its meaning.
c. What assumptions do you have to make about the two populations in order to justify the use of the t test?

10.17 Nondestructive evaluation is a method that is used to describe the properties of components or materials without causing any permanent physical change to the units. It includes the determination of properties of materials and the classification of flaws by size, shape, type, and location. This method is most effective for detecting surface flaws and characterizing surface properties of electrically conductive materials.
Data were collected that classified each component as having a flaw or not, based on manual inspection and operator judgment, and the data also reported the size of the crack in the material. Do the components classified as unflawed have a smaller mean crack size than components classified as flawed? The results in terms of crack size (in inches) are stored in Crack. (Data extracted from B. D. Olin and W. Q.
Meeker, “Applications of Statistical Methods to Nondestructive Evaluation,” Technometrics, 38, 1996, p. 101.)
Type Crack size
0 0.003
0 0.004
0 0.012
0 0.014
0 0.021
0 0.023
0 0.024
0 0.030
0 0.034
0 0.041
0 0.041
0 0.042
0 0.043
0 0.045
0 0.057
0 0.063
0 0.074
0 0.076
1 0.022
1 0.026
1 0.026
1 0.030
1 0.031
1 0.034
1 0.042
1 0.043
1 0.044
1 0.046
1 0.046
1 0.052
1 0.055
1 0.058
1 0.060
1 0.060
1 0.070
1 0.071
1 0.073
1 0.073
1 0.078
1 0.079
1 0.079
1 0.083
1 0.090
1 0.095
1 0.095
1 0.096
1 0.100
1 0.102
1 0.103
1 0.105
1 0.114
1 0.119
1 0.120
1 0.130
1 0.160
1 0.306
1 0.328
1 0.440
a. Assuming that the population variances are equal, is there evidence that the mean crack size is smaller for the unflawed specimens than for the flawed specimens? (Use ? =0.05) b. Repeat (a), assuming that the population variances are not equal.
c. Compare the results of (a) and (b).

10.26 The data in Concrete1 represent the compressive strength, in thousands of pounds per square inch (psi), of 40 samples of concrete taken two and seven days after pouring.
Source: Data extracted from O. Carrillo-Gamboa and R. F. Gunst, “Measurement-Error-Model Collinearities,” Technometrics, 34, 1992, pp. 454–464.
Sample Two Days Seven Days
1 2.830 3.505
2 3.295 3.430
3 2.710 3.670
4 2.855 3.355
5 2.980 3.985
6 3.065 3.630
7 3.765 4.570
8 3.265 3.700
9 3.170 3.660
10 2.895 3.250
11 2.630 2.850
12 2.830 3.340
13 2.935 3.630
14 3.115 3.675
15 2.985 3.475
16 3.135 3.605
17 2.750 3.250
18 3.205 3.540
19 3.000 4.005
20 3.035 3.595
21 1.635 2.275
22 2.270 3.910
23 2.895 2.915
24 2.845 4.530
25 2.205 2.280
26 3.590 3.915
27 3.080 3.140
28 3.335 3.580
29 3.800 4.070
30 2.680 3.805
31 3.760 4.130
32 3.605 3.720
33 2.005 2.690
34 2.495 3.230
35 3.205 3.590
36 2.060 2.945
37 3.425 4.030
38 3.315 3.685
39 3.825 4.175
40 3.160 3.430
a. At the 0.01 level of significance, is there evidence that the mean strength is lower at two days than at seven days?
b. What assumption is necessary about the population distribution in order to perform this test?
c. Find the p-value in (a) and interpret its meaning.

10.46 The Computer Anxiety Rating Scale (CARS) measures an individual’s level of computer
anxiety, on a scale from 20 (no anxiety) to 100 (highest level of anxiety). Researchers at Miami University administered CARS to 172 business students. One of the objectives of the study was to determine whether there is a difference between the level of computer anxiety experienced by female students and male students. They found the following:
Males Females
¯X 40.26 36.85
S 13.35 9.42
n 100 72
Source: Data extracted from T. Broome and D. Havelka, “Determinants of Computer Anxiety in Business Students,” The Review of Business Information Systems, Spring 2002, 6(2), pp. 9–16.
a. At the 0.05 level of significance, is there evidence of a difference in the variability of the computer anxiety experienced by males and females?
b. Interpret the p-value.
c. What assumption do you need to make about the two populations in order to justify the use of the F test?
d. Based on (a) and (b), which t test defined in Section 10.1 should you use to test whether there is a significant difference in mean computer anxiety for female and male students?