1.
The cost of housing for elderly persons who rent as a percentage of income is distributed as listed below.
Beneath the national percentages are the observed frequencies for a random sample of 300 elderly renters
from a the Jacksonville area. At the 0.025 level, could the distribution of housing costs as a percentage of
income for the elderly persons in this area be the same as for the nation as a whole?
National Local Sample
20% to
under 30%
< 20%
National Local
Sample
2.
13.0%
26
25.6%
67
20.3%
68
$ 40%
41.1%
139
100%
n = 300
The following data are the number of persons who were waiting in line at a fast food counter at 100
randomly selected times during the week. At the 0.05 level, test whether the population of these values
could be Poisson distributed.
x = Number
of persons
0
1
2
3
4
5
3.
30% to
under 40%
Number of
Observations
24
24
18
20
10
4
100
A lottery researcher collecting data for an article on his state lottery system, has found the 200 digits most
recently selected to be distributed as shown below. Based on this information, and using the 0.10 level of
significance, can he conclude that the digits have not been drawn from a discrete uniform distribution?
Digit Frequency
0
17
4.
1
18
3
25
4
19
5
16
6
14
7
23
8
24
9
20
200
The following table describes types of collisions versus driving environments for a random sample of twovehicle accidents that occurred in a given region last year. At the 0.01 level of significance, can we
conclude that the type of collision is independent of whether the accident took place in a rural versus an
urban setting?
Driving Urban
Environment Rural
5.
2
24
Angle
Type of Collision
Rear-end
Other
40
6
46
30
12
42
72
15
87
142
33
175
The following contingency table lists the number of financial institutions in various size categories in
selected states. At the 0.01 level of significance, do these data indicate that no relationship exists between
the size of a institution and the state in which it is located?
Under
100
Texas
California
Florida
Assets (millions of dollars)
100 to
300 to
<300
<500
123
79
59
261
94
54
43
191
21
18
8
47
500 to
<1000
1000
or over
22
15
11
48
19
40
27
86
279
206
148
633
6.
What is the purpose of the one-way ANOVA?
7.
A one-way ANOVA has been conducted for an experiment in which there are three treatments and each
treatment group consists of 10 persons. The results include the sum of squares terms shown below. Based
on this information, construct the ANOVA table of summary findings and use the 0.025 level of
significance in testing whether all of the treatment effects could be zero.
SSTR = 252.1
8.
Students in a large section of a biology class have been randomly assigned to one of two graduate students
for the laboratory portion of the class. A random sample of final examination scores has been selected from
students supervised by each graduate student, with the following results:
a.
b.
c.
9.
Grad student A: 78
78
71
89
80
93
73
76
Grad student B: 74
81
65
73
80
63
71
64
50
80
What are the null and alternative hypotheses for this test?
Use ANOVA and the 0.01 level of significance in testing the null hypotheses identified in part (a).
From the F distribution tables. What is the most accurate statement that can be made about the pvalue for this test?
For a two-way ANOVA in which factor A operates on 3 levels and factor B operates on 4 levels, there are 2
replications within each cell. Given the following sum of squares terms, construct the appropriate table of
ANOVA summary findings and use the 0.05 level in examining the null and alternative hypotheses
associated with the experiment.
SSA = 89.58
10.
SSE = 761.1
SSB = 30.17
SSAB = 973.08 SSE = 29.00
Given the following data for a two-way ANOVA, identify the sets of null and alternative hypotheses, then
use the 0.05 level in testing each null hypothesis.
1
2
1
Factor B
2
3
13
10
19
15
19
17
15
22
16
Factor A
11.
12.
15
19
17
Determine the least squares regression line for the following data values, then find the estimated values of y
for x = 6 and x = 9.
x:
2
3
8
10
y:
20
12
7
3
The following data represent x = boat sales and y = boat trailer sales from 1991 through 1996.
Year
1991
1992
1993
1994
1995
1996
a.
b.
c.
13.
Boat Sales (Thousands)
594.5
499.5
570.7
657.7
636.8
660.0
Boat Trailer Sales (Thousands)
190.0
160.0
184.0
200.0
192.0
194.0
Determine the least squares regression line and interpret its slope.
Estimate, for a year during which 620,000 boats are sold, the number of boat trailers that would be
sold.
What reasons might explain why the number of boat trailers sold per year is less than the number
of boats sold per year?
For the 1989 National Football League season, ratings for the leading passers in the National Conference
were as shown below. Also shown for each quarterback is the percentage of passes that were interceptions,
along with the percentage of passes that were touchdowns.
Montana, S.F.
Everett, L.A.
Rypien, Wash.
Hebert, N.O.
Majkowski, G.B.
Simms, N.Y.
Miller, Atl.
Cunningham, Phila.
Wilson, Minn.
Hogeboom, Phoe.
Testaverde, T.B.
Tomczak, Chi.
Gagliano, Det.
Aikman, Dall.
a.
b.
Rating
112.4
90.6
88.1
82.7
82.3
77.6
76.1
75.5
70.5
TD%
6.7%
5.6
4.6
4.2
4.5
3.5
3.0
3.9
2.5
69.5
68.9
68.2
61.2
55.9
Int %
2.1%
3.3
2.7
4.2
3.3
3.5
1.9
2.8
3.3
3.8
4.2
5.2
2.6
3.1
5.2
4.6
5.2
5.2
6.2
Determine the least squares regression line for estimating the passer rating based on the percentage
of passes that were touchdowns.
A quarterback says 5.0% of his passes will be touchdowns next year. Assuming this to be true,
estimate his rating for the coming season.
14.
c.
Determine the standard error of estimate.
The ratings below are based on collision claim experience and theft frequency for 12 makes of small, twodoor cars. Higher numbers reflect higher claims and more frequent thefts, respectively.
Collision:
Theft:
a.
b.
c.
15.
103
103
97 105
113 81
115
68
127
90
104
79
106
97
139
425
110
82
96
81
84
59
105
167
Determine the least squares regression line for predicting the rate of collision claims on the basis
of theft frequency rating.
Calculate and interpret the values of r and r2.
If a new model were to have a theft rating of 110, what would be the predicted rating for collision
claims?
In a proxy statement to stockholders, First Alabama Bancshares, Inc. included the following age and shareownership data for members of the board of directors.
Age
53
60
69
49
67
68
46
a.
b.
c.
Thousands of
Shares Held
7.9
66.4
29.7
60.5
10.4
28.7
86.9
Age
62
63
55
57
71
66
70
Thousands of
Shares Held
121.1
35.3
2.8
74.4
11.1
9.1
19.1
Age
66
57
54
64
56
Thousands of
Shares Held
18.8
3.1
96.5
47.0
31.1
Determine the least squares regression line predicting stock ownership on the basis of age.
Determine and interpret the coefficients of correlation and determination.
If a board member were 64 years of age, what would be the predicted number of shares owned?
16.
For the regression analysis of the data in number 15.
a.
Use the 0.05 level in testing whether the population coefficient of correlation could be zero.
b.
Use the 0.10 level in testing whether the population regression equation could have a slope of zero.
c.
Construct the 90% confidence interval for the slope of the population regression equation. Discuss
the interval in terms of the results of part (b).
17.
The owner of a large chain of health spas has selected eight of her smaller clubs for a test in which she
varies the size of the newspaper ad and the amount of the initiation fee discount to see how this might affect
the number of prospective members who visit each club during the following week. The results are shown
on the below.
Club
1
2
3
4
5
6
7
New
Visitors, y
23
30
20
26
20
18
17
Ad ColumnInches, x1
4
7
3
6
2
5
4
Discount
Amount, x2
$100
20
40
25
50
30
25
8
a.
b.
c.
31
8
80
Use MyStat to determine the least squares multiple regression equation.
Interpret the y-intercept and partial regression coefficients.
What is the estimated number of new visitors to a club if the size of the ad is 5 column-inches and
a $75 discount is offered?
18.
The multiple regression equation, y^ = 10 + 3x1 - 2x2 + 14x3, has been fitted to a set of 18 data points. The
sum of the squared differences between observed and predicted values of y has been calculated as SSE =
200.0. The sum of squared differences between y values and the mean of y is SST = 900. What is the
multiple standard error of estimate?
19.
For a given regression analysis, the sum-of-squares terms have been calculated as SST = 342.5, SSR =
200.0, and SSE = 142.5. Determine the value of R2 and interpret its meaning.
20.
Interested in the possible relationship between the size of his tip versus the size of the check and the number
of diners in the party, a food server has recorded the following for a sample of 8 checks:
Observation
Number
1
2
3
4
5
6
7
8
a.
b.
c.
d.
e.
f.
y = Tip
$7.5
0.5
2.0
3.5
9.5
2.5
3.5
1.0
x1 = Check
$40
15
30
25
50
20
35
10
x2 = Diners
2
1
3
4
4
5
5
2
Using MyStat, determine the multiple regression equation. Interpret the partial regression
coefficients.
What is the estimated tip amount for 3 diners who have a $40 check?
Determine the 95% prediction interval for the tip left by a dining party like the one in part (b).
Determine the 95% confidence interval for the mean tip left by all dining parties like the one in
part (b).
Determine the 95% confidence interval for the partial regression coefficients, β 1 and β2.
Interpret the significance tests in the computer printout.
21.
The estimated trend value of community water consumption is 400,000 gallons for a given month.
Assuming that the cyclical component is 120% of normal, with the seasonal and irregular components 70%
and 110% of normal, respectively, use the multiplicative time series model in determining the quantity of
water consumed during the month.
22.
Fit a linear trend equation to the following data describing average hourly earnings in the metal-cutting
machine tools industry.1 What is the trend estimate for 1994?
Year:
1985
Average hourly earnings: $12.42
23.
1986
1987
1988
$12.78
$12.90
$13.05
A management consulting firm consists of three partners, whose number of clients and average fee per
client were as shown below for 1988 through 1990:
1988
1989
1990
a.
b.
24.
C
3
4
2
Average Billing
per Client
B
$15,000
$20,000
$10,000
A
$2,500
$1,500
$3,000
C
$65,000
$50,000
$80,000
Using 1988 as the base period, what is the simple aggregate price index for clients served in 1989?
In 1990?
Using 1988 as the base period, what is the simple aggregate quantity index for the number of
clients served in 1989? In 1990?
U.S. brick shipments from 1977 through 1988 are represented by the following index numbers. Convert the
index numbers so that the base period will be 1984 instead of 1980.
1977
1978
1979
1980
1981
1982
25.
Number of
Clients Served
A
B
8
10
10
8
15
12
142.6
141.0
126.2
100.0
83.6
83.6
1983
1984
1985
1986
1987
1988
101.6
114.8
111.5
121.3
119.7
116.4
The following table summarizes the unit sales and prices for Norman=s Nuts from 1987 through 1990:
1987
1988
1989
1990
Pounds Sold
Cashews Hot Mix Macadamia Nuts
1240
140
40
1310
200
400
1400
160
520
1950
850
840
Price per Pound
Cashews Hot Mix Macadamia Nuts
$7.50
$4.00
$8.00
$6.00
$9.50
$7.50
$11.00
$8.00
$14.00
$16.00
$19.50
$23.00
Using 1987 as the base period, construct
a.
A Paasche price index for each year.
b.
A Laspeyres price index for each year.
c.
A fixed-weight aggregate price index for each year. For weighting, use the average annual number
of pounds sold for each type of nut during the 1988-89 period.