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These
problems all draw on data that come
from the text ( or a previous edition).
If you are ready for the test you should recognize what to do. The advantage of this format is that you
cannot see what to do by looking at previous pages of the text. See if you are ready. But
if you are not, use the hints and study the material again.
1)
The data below are stress scores for random samples of people
who work
in three occupations. Use the data to
test for a difference in the mean stress level among the occupations. a
= .05.
Real Estate Agent |
Architect |
Stockbroker |
81 |
43 |
65 |
48 |
63 |
48 |
68 |
60 |
57 |
69 |
52 |
91 |
54 |
54 |
70 |
62 |
77 |
67 |
76 |
68 |
83 |
56 |
57 |
75 |
61 |
61 |
53 |
65 |
80 |
71 |
64 |
50 |
54 |
69 |
37 |
72 |
83 |
73 |
65 |
85 |
84 |
58 |
75 |
58 |
58 |
2) a) The
data below give P/E ratios for random samples of corporations in three
industries. Use the data to test for a
difference in the
mean ratios. alpha = .05.
Company |
Industry |
P/E |
Citicorp |
1 |
15 |
NationsBank |
1 |
14 |
Wells
Fargo |
1 |
25 |
First
Union |
1 |
13 |
KeyCorp |
1 |
14 |
Chase
Manhattan |
1 |
12 |
Fifth
Third Bancorp |
1 |
23 |
Bank
of New York |
1 |
17 |
First
Chicago |
1 |
3 |
Mellon
Bank |
1 |
16 |
Fleet
Financial Group |
1 |
15 |
First
Bank System |
1 |
16 |
American
Express |
2 |
19 |
Travelers |
2 |
15 |
Merrill
Lynch |
2 |
12 |
MBNA |
2 |
24 |
Cincinnati
Financial |
2 |
19 |
Franklin
Resources |
2 |
22 |
Fannie
Mae |
2 |
17 |
American
International Group |
3 |
21 |
Allstate |
3 |
14 |
Marsh
& McLennan |
3 |
20 |
American
General |
3 |
16 |
Cigna |
3 |
12 |
Lincoln
National |
3 |
13 |
AFLAC |
3 |
21 |
Equitable |
3 |
11 |
Chubb |
3 |
20 |
General
Re |
3 |
15 |
2b) Construct all
pairwise differences in the industry means at the 95 % level of
confidence,
using the simple LSD method. hint
2c) Construct all
pairwise differences in the industry means at the 94 % level of
confidence,
using the Bonferroni method. hint
3) Five automobiles
were used to compare gasoline mileage for three gas types.
Miles per gallon for the three gasoline
types are given for each of the five automobiles. Test
the hypothesis appropriate to the data. a =
.01. hint
|
|
|
Gasoline |
|
|
|
I |
II |
III |
|
Art’s
car |
18 |
21 |
20 |
|
Bob’s
car |
24 |
26 |
27 |
autos |
Carl’s
car |
30 |
29 |
34 |
|
Dave’s
car |
22 |
25 |
24 |
|
Ed’s
car |
20 |
23 |
24 |
4) Use the data below to conduct a two factor AOV for the effect of position and experience
on salary. Allow for
interaction, a = .05. hint
Observation |
Salary ($) |
Position |
Experience |
1 |
28,938 |
Inside |
Medium |
2 |
27,694 |
Inside |
Medium |
3 |
45,515 |
Outside |
Low |
4 |
27,031 |
Inside |
Medium |
5 |
37,283 |
Outside |
Low |
6 |
32,718 |
Inside |
Low |
7 |
54,081 |
Outside |
High |
8 |
23,621 |
Inside |
Low |
9 |
47,835 |
Outside |
High |
10 |
29,768 |
Inside |
Medium |
11 |
27,282 |
Inside |
Medium |
12 |
30,632 |
Inside |
Low |
13 |
38,856 |
Outside |
Low |
14 |
26,827 |
Inside |
Medium |
15 |
26,948 |
Inside |
Low |
16 |
31,588 |
Inside |
Medium |
17 |
43,858 |
Outside |
Low |
18 |
38,478 |
Outside |
Low |
19 |
58,846 |
Outside |
Medium |
20 |
34,253 |
Inside |
High |
21 |
28,464 |
Inside |
Low |
22 |
58,176 |
Outside |
Medium |
23 |
35,949 |
Inside |
High |
24 |
27,833 |
Inside |
Low |
25 |
47,914 |
Outside |
High |
26 |
58,040 |
Outside |
Medium |
5) a) Use the table below to test all possible hypotheses.
b) How does your
answer change if the rows identify blocks? hint
ANOVA |
|
|
|
|
|
|
Source of
Variation |
SS |
df |
MS |
F |
P-value |
F crit |
Rows |
2795.6 |
9 |
310.6222222 |
1.05510266 |
0.42506065 |
2.25013252 |
Columns |
19805.2 |
3 |
6601.733333 |
22.4243659 |
1.7029E-07 |
2.96034841 |
Error |
7948.8 |
27 |
294.4 |
|
|
|
|
|
|
|
|
|
|
Total |
30549.6 |
39 |
|
|
|
|
6) a) Use the data below to test the hypothesis that no load mutual funds have the same return that load funds do.
b) Construct a confidence interval for the
difference in the
mean returns. hint
Mutual Funds - Load |
Return |
|
Mutual Funds - No Load |
Return |
American
National Growth |
15.51 |
|
Amana
Income Fund |
13.24 |
Arch
Small Cap Equity |
14.57 |
|
Berger
One Hundred |
12.13 |
Bartlett
Cap Basic |
17.73 |
|
Columbia
International Stock |
12.17 |
Calvert
World International |
10.31 |
|
Dodge
& Cox Balanced |
16.06 |
Colonial
Fund A |
16.23 |
|
Evergreen
Fund |
17.61 |
Common
Sense Growth |
16.04 |
|
Fidelity
Fund |
20.61 |
Corefund
Core Equity |
18.77 |
|
Forthis
Advtg Cap App |
13.38 |
Davis
Convert Seurities |
18.21 |
|
Founders
Blue Chip Fund |
17.15 |
Deleware
Small Cap |
17.27 |
|
Goldman
Core Fixed Income |
10.38 |
Dreyfus
Premium Value |
11.95 |
|
Heartland
Value |
18.15 |
Federated
Stocks & Bonds |
13.81 |
|
Janus
Fund |
15.82 |
First
Invest FD for Income |
12.44 |
|
Manstay
Cap Appriciation |
17.29 |
7) The data below
give earnings in 97 matched to those in 96 for the firms listed. Use
the data to test the hypothesis that mean
earnings in
96 and 97 were the same. hint
b) Construct a confidence interval for the difference in the mean earnings.
Company |
Earnings 96 |
Earnings 97 |
Atlantic
Richfield |
1.16 |
1.17 |
Balchem
Corp |
0.16 |
0.13 |
Black
& Decker Corp |
0.97 |
1.02 |
Dial
Corp |
0.18 |
0.23 |
DSC
Communications |
0.15 |
-0.32 |
Eastman
Chemical |
0.77 |
0.36 |
Excel
Communications |
0.28 |
-0.14 |
Federal
Signal |
0.40 |
0.29 |
Ford
Motor Company |
0.97 |
1.45 |
GTE
Corp |
0.81 |
0.73 |
ITT
Industries |
0.59 |
0.6 |
Kimberly-Clark |
0.61 |
-0.27 |
Minnesota
Mining & Mfr. |
0.91 |
0.89 |
Procter
& Gamble |
0.63 |
0.71 |
8) a)
These are random samples of values
of the DJIA in November and December. Test
the hypothesis that this value is
equally variable in the two time periods. hint
b) Test the hypothesis that the population mean of
this value
is equal in the two time periods. hint
November |
December |
7493 |
8066 |
7525 |
8209 |
7760 |
7842 |
7499 |
7943 |
7555 |
7846 |
7690 |
8071 |
7668 |
8055 |
7600 |
8159 |
7516 |
7828 |
7711 |
8109 |
9) You should be
able to interpret all of this printout. hint
SUMMARY
OUTPUT |
|
|
|
|
|
|
|
|
|
Regression
Statistics |
|
|
|
|
Multiple
R |
0.735101 |
|
|
|
R
Square |
0.540374 |
|
|
|
Adjusted
R Square |
0.425467 |
|
|
|
Standard
Error |
14.16456 |
|
|
|
Observations |
16 |
|
|
|
|
|
|
|
|
ANOVA |
|
|
|
|
|
df |
SS |
MS |
F |
Regression |
3 |
2830.58625 |
943.52875 |
4.70271908 |
Residual |
12 |
2407.6167 |
200.634725 |
|
Total |
15 |
5238.20295 |
|
|
|
|
|
|
|
|
Coefficients |
Standard
Error |
t
Stat |
P-value |
Intercept |
-179.973 |
112.858543 |
-1.5946793 |
0.13676805 |
Curb
Weight (lb.) |
-0.01431 |
0.0167821 |
-0.8524396 |
0.41066111 |
Horsepower |
-0.15314 |
0.14947024 |
-1.0245438 |
0.32578912 |
Speed
at 1/4 mile (mph) |
3.141385 |
1.29764869 |
2.42082886 |
0.03226857 |