1. Consider a
multinomial experiment involving n = 300 and k = 5 cells. The observed frequencies resulting from the
experiment are shown in the companying table, and the null hypothesis to be
tested is as follows:
Ho P1= .1, P2= .2, P3 = .3, P4 = .2 , P5 = .2
Test the hypothesis at the 1% significance level.
Cell 1 2
3 4 5
Frequency
24 64 84
72 56
2. A random
sample of 50 observations yielded the following frequencies for the
standardized intervals:
Interval
Frequency
Z ? -1
6
-1 < Z ?0 27
0 < Z ?1
14
Z >
1
3
Can we infer that the data are not normal? Use
? =.10
3. Conduct a
test to determine whether the two classifications r and c are independent,
using the data in the following contingency table. Use
? =.10.
C1 C2 C3
R1
40 32 48
R2 30 48 52
4. University
students often complain that universities reward professors for research, but
not for teaching, and argue that professors react to this situation by devoting
more time and energy to the publication of their findings and less time and
energy to classroom activities.
Professors counter that research and teaching go hand in hand: More research makes better teachers. A student organization at one university
decided to investigate the issue. They
randomly selected 50 economics professors who are employed by a multi-campus
university. The students recorded the
salaries (in $ thousands) of the professors, their average teaching evaluations
(on a 10-point scale), and the total number of journal articles published in
their careers. Perform a complete
analysis (produce the regression equation, access it, and report your
findings). Data are listed below. Use a 5% significance level.
|
Salary |
Evaluation |
Articles |
|
41.5 |
5.19 |
0 |
|
82.1 |
6.77 |
12 |
|
60 |
6.34 |
9 |
|
57.1 |
5.76 |
6 |
|
54.2 |
6.46 |
3 |
|
61.5 |
6.23 |
12 |
|
63.2 |
6.38 |
16 |
|
63.2 |
6.45 |
0 |
|
49.2 |
7.2 |
2 |
|
75.7 |
8.16 |
31 |
|
65.6 |
6.49 |
3 |
|
63.9 |
6.28 |
9 |
|
57 |
5.39 |
3 |
|
63.2 |
8.25 |
8 |
|
82.9 |
6.53 |
21 |
|
103.3 |
8.46 |
42 |
|
83.7 |
9.48 |
29 |
|
59.5 |
7.01 |
4 |
|
65.7 |
6.8 |
11 |
|
52.3 |
6.2 |
7 |
|
70.4 |
6.01 |
20 |
|
58.1 |
6.24 |
5 |
|
75 |
7.99 |
22 |
|
49.9 |
5.58 |
1 |
|
85 |
6.93 |
28 |
|
88.4 |
7.35 |
22 |
|
58.4 |
5.81 |
2 |
|
83 |
7.18 |
16 |
|
77.3 |
7.38 |
18 |
|
50.9 |
5.74 |
4 |
|
57 |
6.61 |
4 |
|
45.5 |
7.4 |
4 |
|
51.1 |
5.83 |
1 |
|
69.8 |
6.85 |
8 |
|
60.3 |
6.63 |
9 |
|
55.3 |
5.23 |
5 |
|
61.8 |
5.4 |
14 |
|
50.5 |
6.52 |
15 |
|
80.1 |
7.39 |
34 |
|
71.1 |
7.77 |
19 |
|
59.6 |
5.06 |
5 |
|
59.2 |
4.31 |
1 |
|
52 |
5.83 |
0 |
|
87.2 |
6.48 |
23 |
|
65.3 |
5.5 |
14 |
|
49.8 |
5.13 |
2 |
|
58 |
6.14 |
9 |
|
74.2 |
6.88 |
14 |
|
65.7 |
5.02 |
9 |
|
60 |
6.05 |
4 |
5. A study
performed by a Columbia University professor (descried in Report on Business,
august 1991) counted the number of times per minute professors from three
different departments said “uh” or “ah” during lectures to fill gaps between
words. The data derived from observing
100 minutes from each of the three departments were recorded. If we assume that the more frequent use of
“uh” or “ah” results in more boring lectures, can we conclude that some
departments’ professors were more boring than others? Data recorded below:
|
English |
Mathematics |
Political |
|
4 |
1 |
5 |
|
9 |
8 |
4 |
|
8 |
4 |
9 |
|
7 |
6 |
5 |
|
4 |
7 |
5 |
|
4 |
8 |
5 |
|
8 |
5 |
6 |
|
7 |
4 |
4 |
|
9 |
4 |
5 |
|
0 |
5 |
5 |
|
7 |
0 |
4 |
|
4 |
2 |
0 |
|
7 |
6 |
6 |
|
8 |
6 |
7 |
|
4 |
6 |
4 |
|
4 |
3 |
3 |
|
7 |
5 |
3 |
|
5 |
5 |
6 |
|
0 |
4 |
7 |
|
3 |
4 |
4 |
|
3 |
4 |
5 |
|
1 |
9 |
1 |
|
3 |
8 |
8 |
|
3 |
5 |
9 |
|
4 |
8 |
5 |
|
7 |
7 |
9 |
|
10 |
1 |
4 |
|
8 |
6 |
7 |
|
7 |
7 |
0 |
|
5 |
3 |
9 |
|
1 |
5 |
5 |
|
5 |
5 |
6 |
|
3 |
7 |
4 |
|
4 |
1 |
5 |
|
5 |
7 |
5 |
|
10 |
5 |
6 |
|
5 |
3 |
5 |
|
8 |
8 |
5 |
|
4 |
5 |
3 |
|
4 |
4 |
4 |
|
4 |
5 |
5 |
|
9 |
7 |
6 |
|
5 |
6 |
4 |
|
9 |
5 |
3 |
|
5 |
3 |
8 |
|
7 |
4 |
3 |
|
3 |
5 |
5 |
|
8 |
8 |
7 |
|
10 |
7 |
8 |
|
4 |
6 |
8 |
|
8 |
5 |
6 |
|
11 |
5 |
7 |
|
5 |
4 |
3 |
|
7 |
6 |
8 |
|
4 |
8 |
3 |
|
8 |
3 |
6 |
|
5 |
9 |
5 |
|
8 |
6 |
4 |
|
3 |
8 |
4 |
|
7 |
6 |
6 |
|
8 |
7 |
4 |
|
8 |
2 |
8 |
|
7 |
3 |
3 |
|
7 |
5 |
6 |
|
5 |
2 |
8 |
|
4 |
5 |
4 |
|
10 |
5 |
7 |
|
4 |
4 |
7 |
|
5 |
7 |
6 |
|
4 |
6 |
8 |
|
4 |
7 |
2 |
|
4 |
4 |
7 |
|
4 |
9 |
2 |
|
7 |
9 |
6 |
|
10 |
6 |
4 |
|
7 |
5 |
8 |
|
2 |
9 |
2 |
|
5 |
2 |
6 |
|
5 |
8 |
6 |
|
5 |
7 |
5 |
|
8 |
4 |
5 |
|
8 |
3 |
3 |
|
10 |
6 |
4 |
|
5 |
4 |
2 |
|
9 |
5 |
6 |
|
1 |
5 |
7 |
|
7 |
7 |
4 |
|
8 |
4 |
5 |
|
5 |
6 |
8 |
|
7 |
1 |
5 |
|
7 |
3 |
4 |
|
9 |
7 |
8 |
|
8 |
6 |
6 |
|
5 |
6 |
8 |
|
8 |
5 |
7 |
|
1 |
6 |
6 |
|
5 |
5 |
5 |
|
7 |
5 |
7 |
|
7 |
8 |
5 |
|
2 |
5 |
8 |
*NOTE* Frequent use of “uh” and “ah” could signify
nervousness, a lack of rehearsal, or speaking without a memorized script, it
should not automatically mean the professor is boring. However, it serves as a distractor. It could be annoying, and unappealing. The listener will be so attuned to each “ah”
and “uh” that he or she will focus on that, and away from the lecture
itself. That could lead to the belief
that the lecture is boring.
6. A
newspaper publisher, trying to pinpoint his market’s characteristics, wondered
whether the way people read a newspaper is related to the reader’s educational
level. A survey asked adult readers
which section of the paper they read first, and asked to report their highest
educational level. These data were
recorded (column 1 = first section read where 1 = front page, 2 = sports, 3 =
editorial, and 4 = other; and column 2 = educational level where 1 = did not
complete high school, 2 = high school graduate, 3 = university or college
graduate, and 4 = post graduate degree).
Is there sufficient evidence to conclude that the four methods differ in
their success? Data below:
|
Section |
Education |
|
4 |
2 |
|
2 |
2 |
|
4 |
2 |
|
4 |
3 |
|
4 |
2 |
|
1 |
4 |
|
1 |
3 |
|
1 |
2 |
|
4 |
1 |
|
2 |
2 |
|
2 |
3 |
|
4 |
3 |
|
2 |
2 |
|
4 |
1 |
|
2 |
3 |
|
3 |
3 |
|
4 |
3 |
|
1 |
3 |
|
3 |
3 |
|
4 |
2 |
|
1 |
4 |
|
2 |
4 |
|
1 |
2 |
|
2 |
2 |
|
1 |
2 |
|
2 |
1 |
|
2 |
2 |
|
3 |
3 |
|
1 |
4 |
|
3 |
3 |
|
1 |
2 |
|
1 |
4 |
|
2 |
4 |
|
3 |
3 |
|
4 |
2 |
|
3 |
3 |
|
1 |
4 |
|
1 |
2 |
|
2 |
2 |
|
2 |
3 |
|
1 |
3 |
|
2 |
1 |
|
3 |
3 |
|
4 |
2 |
|
3 |
3 |
|
4 |
2 |
|
2 |
2 |
|
1 |
4 |
|
4 |
2 |
|
3 |
3 |
|
1 |
2 |
|
2 |
2 |
|
4 |
2 |
|
3 |
2 |
|
3 |
3 |
|
2 |
2 |
|
2 |
3 |
|
3 |
4 |
|
4 |
2 |
|
4 |
2 |
|
2 |
3 |
|
1 |
3 |
|
3 |
3 |
|
4 |
1 |
|
3 |
3 |
|
2 |
1 |
|
4 |
2 |
|
1 |
3 |
|
1 |
3 |
|
4 |
1 |
|
2 |
1 |
|
2 |
1 |
|
3 |
2 |
|
3 |
2 |
|
2 |
1 |
|
3 |
3 |
|
3 |
4 |
|
1 |
4 |
|
4 |
2 |
|
4 |
2 |
|
1 |
3 |
|
4 |
3 |
|
4 |
3 |
|
4 |
2 |
|
1 |
3 |
|
1 |
3 |
|
2 |
1 |
|
2 |
1 |
|
1 |
3 |
|
3 |
4 |
|
4 |
2 |
|
2 |
1 |
|
3 |
3 |
|
2 |
1 |
|
4 |
2 |
|
4 |
2 |
|
2 |
2 |
|
4 |
2 |
|
4 |
2 |
|
2 |
2 |
|
3 |
3 |
|
2 |
2 |
|
2 |
1 |
|
1 |
3 |
|
1 |
4 |
|
1 |
2 |
|
3 |
2 |
|
3 |
3 |
|
2 |
2 |
|
3 |
2 |
|
4 |
3 |
|
4 |
2 |
|
4 |
3 |
|
3 |
2 |
|
1 |
3 |
|
3 |
2 |
|
4 |
3 |
|
1 |
2 |
|
4 |
2 |
|
1 |
2 |
|
4 |
2 |
|
4 |
1 |
|
2 |
1 |
|
3 |
4 |
|
2 |
2 |
|
1 |
3 |
|
1 |
3 |
|
2 |
1 |
|
2 |
1 |
|
2 |
1 |
|
1 |
3 |
|
3 |
4 |
|
2 |
3 |
|
3 |
4 |
|
1 |
1 |
|
2 |
3 |
|
1 |
1 |
|
3 |
3 |
|
1 |
4 |
|
3 |
2 |
|
4 |
2 |
|
4 |
3 |
|
3 |
4 |
|
3 |
4 |
|
4 |
3 |
|
4 |
2 |
|
3 |
4 |
|
3 |
3 |
|
3 |
3 |
|
2 |
2 |
|
4 |
2 |
|
3 |
2 |
|
4 |
4 |
|
4 |
1 |
|
1 |
3 |
|
1 |
3 |
|
4 |
3 |
|
2 |
2 |
|
4 |
3 |
|
1 |
4 |
|
3 |
2 |
|
3 |
3 |
|
3 |
3 |
|
3 |
3 |
|
3 |
4 |
|
2 |
1 |
|
2 |
1 |
|
2 |
1 |
|
2 |
3 |
|
4 |
1 |
|
2 |
1 |
|
1 |
2 |
|
2 |
3 |
|
2 |
1 |
|
3 |
3 |
|
2 |
2 |
|
3 |
3 |
|
3 |
4 |
|
3 |
2 |
|
3 |
4 |
|
3 |
3 |
|
3 |
3 |
|
2 |
3 |
|
3 |
2 |
|
2 |
3 |
|
3 |
3 |
|
4 |
2 |
|
3 |
2 |
|
1 |
4 |
|
2 |
1 |
|
3 |
4 |
|
3 |
2 |
|
3 |
2 |
|
2 |
2 |
|
1 |
3 |
|
4 |
2 |
|
1 |
3 |
|
3 |
3 |
|
1 |
2 |
|
2 |
2 |
|
1 |
3 |
|
3 |
4 |
|
4 |
2 |
|
4 |
2 |
|
1 |
3 |
|
3 |
4 |
|
4 |
3 |
|
4 |
3 |
|
1 |
2 |
|
4 |
3 |
|
4 |
2 |
|
3 |
4 |
|
4 |
3 |
|
3 |
3 |
|
1 |
4 |
|
3 |
4 |
|
1 |
4 |
|
1 |
2 |
|
3 |
3 |
|
3 |
2 |
|
2 |
2 |
|
4 |
2 |
|
4 |
4 |
|
4 |
2 |
|
4 |
2 |
|
2 |
1 |
|
2 |
2 |
|
2 |
1 |
|
2 |
2 |
|
2 |
2 |
|
4 |
1 |
|
3 |
3 |
|
1 |
3 |
|
1 |
1 |
|
3 |
3 |
|
3 |
3 |
|
2 |
2 |
|
1 |
2 |
|
3 |
3 |
|
3 |
4 |
|
4 |
4 |
|
1 |
3 |
|
3 |
4 |
|
2 |
2 |
|
4 |
1 |
|
4 |
2 |
|
2 |
3 |
|
1 |
2 |
|
1 |
2 |
|
3 |
3 |
|
4 |
2 |
|
3 |
3 |
|
2 |
3 |
|
2 |
3 |
|
1 |
3 |
|
3 |
2 |
|
1 |
3 |
|
3 |
1 |
|
2 |
1 |
|
1 |
3 |
|
1 |
2 |
|
4 |
3 |
|
1 |
2 |
|
4 |
2 |
|
2 |
3 |
|
3 |
3 |
|
4 |
2 |
|
1 |
3 |
|
4 |
3 |
|
3 |
4 |
|
4 |
2 |
|
3 |
2 |
|
2 |
2 |
|
4 |
1 |
|
4 |
3 |
|
4 |
3 |
|
2 |
2 |
|
1 |
2 |
|
2 |
2 |
|
1 |
3 |
|
1 |
1 |
|
3 |
3 |
|
2 |
2 |
|
4 |
2 |
|
2 |
1 |
|
3 |
4 |
|
4 |
3 |
|
3 |
3 |
|
3 |
3 |
|
2 |
2 |
|
4 |
2 |
|
2 |
3 |
|
3 |
4 |
|
1 |
3 |
|
3 |
3 |
|
2 |
3 |
|
3 |
3 |
|
1 |
3 |
|
2 |
2 |
|
1 |
3 |
|
3 |
2 |
|
2 |
1 |
|
4 |
3 |
|
4 |
2 |
|
3 |
2 |
|
1 |
2 |
|
2 |
2 |
|
1 |
4 |
|
4 |
2 |
|
2 |
1 |
|
1 |
2 |
|
2 |
3 |
|
4 |
2 |
*NOTE* There
could be various factors that affect how a reader reads the newspaper. They may not start with the same section each
time. There could be a reason for
beginning with the sports section on one day, and the editorial on
another. The survey did not include
these variables. If they were not
factored in, the data gathered by the survey would be inconclusive.
7. A
statistics practitioner conducted a two-factor analysis of variance experiment
with a = 4, b = 3,
and r = 8.
The sum of the squares are listed here:
SS(total)
= 9420 SS(A) = 203 SS(B) = 859 SS(AB) = 513
a. Test at the 5% significance level to determine
whether factors a andb interact.
b. Test at the 5% significance level to
determine whether differences exist between the levels of factor a.
c. Test at the 5% significance level to
determine whether differences exist between the levels of factor b.
8. To determine how the number of housing starts
is affected by mortgage rates, an economist recorded the average mortgage rate
and number of housing starts in a large country for the past 10 years. These data are listed here: (*NOTE: The CD reflects “8” as the last
“Rate” entry, instead of “9.0” as it
shows in the Unit Assessment .”)
Rate: 8.5
78 7.6 7.5
8.0 8.4 8.8
8.9 8.5 9.0
Starts: 115
111 185 201
206 167 155
117 133 150
a.) Determine the regression line.
b.) What do the coefficients of the regression
line tell you about the relationship between mortgage rates and housi
