Unformatted Attachment Preview
1.
value:
2.50 points
(Use Excel) A recent survey by Genworth Financial Inc., a financial-services company, concludes that the
cost of long-term care in the United States varies significantly, depending on where an individual lives (The
Wall Street Journal, May 16, 2009). An economist collects data from the five states with the highest annual
costs (Alaska, Massachusetts, New Jersey, Rhode Island, and Connecticut) in order to determine if his
sample data are consistent with the survey's conclusions. The economist provides the following portion of
an ANOVA table. Use Table 4:
a. Complete the ANOVA table. Assume that long-term care costs are normally distributed. (Leave no cells
blank - be certain to enter "0" wherever required. Round your answers except "df" to 2 decimal
places.)
MS
F
p-value
Fcrit at 5%
ANOVA
Source of Variation
Between Groups
Within Groups
SS
635.0542
df
4
253.2192
20
Total
888.2734
24
b. Specify the competing hypotheses to test whether some differences exist in the mean long-term care
costs in these five states.
Ho PAlaska = Massachusetts = PNew Jersey = PRhode Island = P Connecticut. Ha; Not all population
means are equal.
Ho: PAlaska SP Massachusetts SH New Jersey - PRhode Island SPConnecticut. HA; Not all population
means are equal.
Ho: PAlaskaMassachusetts - PNew Jersey ? PRhode Island Connecticut. Hai Not all population
means are equal.
c. At the 5% significance level, can we conclude that mean costs differ?
Yes, since the p-value is less than a.
Yes, since the p-value is not less than a.
No, since the p-value is less than a.
No, since the p-value is not less than a.
OC
3.
value:
2.50 points
(Round all intermediate calculations to at least 4 decimal places.)
The following statistics are computed by sampling from three normal populations whose variances are
equal: Use Table 2 and Table 5.
X1 = 22.6, n1 = 6;
X2 = 30.1, n2 = 8;
X3 = 34.0, n3 = 5;
MSE = 28.7
a. Use Fisher's LSD test to determine which population means differ at 95% confidence intervals.
(Negative values should be indicated by a minus sign. Round your answers to 2 decimal places.)
Population Mean
Differences
P1 P2
Confidence Interval
[
[
]
]
Can we conclude that the
population means differ?
(Click to select)
(Click to select) 4
(Click to select) 4
1-M3
9
23
[
]
b. Repeat the analysis with Tukey's HSD approach. (If the exact value for nt - c is not found in the
table, use the value which is closer. Negative values should be indicated by a minus sign. Round
your answers to 2 decimal places.)
Population Mean
Differences
1 - 2
Confidence Interval
]
]
Can we conclude that the
population means differ?
(Click to select)
(Click to select)
(Click to select)
13
12 - 3
[
c. Which of these two approaches would you use to determine whether differences exist between the
population means?
Tukey's HSD
Fisher's LSD
4.
value:
2.50 points
(Round all intermediate calculations to at least 4 decimal places.)
Do energy bills vary dramatically depending on where you live in the United States? Suppose 25
households from four regions in the United States are sampled. The values for the average annual energy
bill are shown below and are consistent with those found by The Department of Energy (Money, June
2009). Use Table 5.
Region
Average annual
Energy bill
West
$1,491
Northeast
$2,319
Midwest
$1,768
South
$1,758
A portion of the ANOVA calculations are below:
ANOVA
Source of Variation
Between Groups
Within Groups
SS
7531769
3492385
df
3
96
MS
?
?
F
?
p-value
7.13E-24
Total
11024154
99
a. Complete the ANOVA table. (Round your answers to 2 decimal places.)
df
MS
F
ANOVA
Source of Variation
Between Groups
Within Groups
SS
7531769
p-value
7.13E-24
3
3492385
96
Total
11024154
99
5.
value:
2.50 points
(Round all intermediate calculations to at least 4 decimal places.)
The following observations were obtained when conducting a two-way ANOVA experiment with no
interaction. Use Table 4
Click here for the Excel Data File
Factor B
1
2
3
Xi for Factor A
1
3
8
12
7.667
Factor A
2
3
4
3
10
9
16
14
10.000
8.667
4
5
8.
13
8.667
Xj for Factor B
3.750
8.750
13.750
X = 8.750
a. Calculate SST, SSA, SSB, and SSE. (Round your answers to 2 decimal places.)
,SST
SSA
SSB
SSE
b. Calculate MSA, MSB, and MSE. (Round your answers to 2 decimal places.)
MSA
MSB
MSE
2
2
10
9
9
13
11
XI = 10.1250
si = 2.4107
11
9
10
10
11
8
*2 = 9.7500
sź = 1.0714
I
= 9.5000
10
9
8
7
8.
9
x3 = 8.6250
să = 0.8393
a. Construct an ANOVA table. Assume production rates are normally distributed. (Round SS, MS, and F
to 2 decimal places and p-value to 4 decimal places.)
df
MS
F
ANOVA
Source of Variation
Between Groups
Within Groups
SS.
9.75
p-value
0.072058
2
4.875
2.989051
34.25
21
1.630952
Total
44
23
b. Specify the competing hypotheses to test whether there are some differences in the mean production
rates across the three assembly lines.
Ho: PRazor = Blazer = H Tracer. Ha: Not all population means are equal.
Ho: Prazor s Blazers Tracer. Ha: Not all population means are equal
Ho: PRazor Blazer Tracer. Ha: Not all population means are equal.
C-1. At the 5% significance level, what is the conclusion of the test?
A conclude that the mean buggies/hour differs for
Do not reject
Ho, we cannot
some production lines.
C-2. What about the 10% significance level?
can
conclude that the mean buggies/hour differs for
Reject HO
4 Ho, we
some production lines.
2.
value:
2.50 points
(Round all intermediate calculations to at least 4 decimal places.)
Wenton Powersports produces dune buggies. They have three assembly lines, "Razor,” “Blazer," and
"Tracer," named after the particular dune buggy models produced on those lines. Each assembly line was
originally designed using the same target production rate. However, over the years, various changes have
been made to the lines. Accordingly, management wishes to determine whether the assembly lines are still
operating at the same average hourly production rate. Production data (in dune buggies/hour) for the last
eight hours are as follows.
Razor
11
10
8
10
9
9
13
11
X1 = 10.1250
si = 2.4107
Blazer
10
9
11
9
10
10
11
8
*2 = 9.7500
sź = 1.0714
X = 9.5000
Tracer
9
9
10
9
8
7
8
9
X3 = 8.6250
s3 = 0.8393
a. Construct an ANOVA table. Assume production rates are normally distributed. (Round SS, MS, and F
to 2 decimal places and p-value to 4 decimal places.)
df
MS
ANOVA
Source of Variation
Between Groups
Within Groups
SS
9.75
F
2.989051
p-value
0.072058
2
4.875
34.25
21
1.630952
44
Total
23
6.
value:
2.50 points
(Round all intermediate calculations to at least 4 decimal places.)
The following output summarizes a portion of the results for a two-way analysis of variance experiment with
no interaction. Factor A consists of four different kinds of organic fertilizers, factor B consists of three
different kinds of soil acidity levels, and the variable measured is the height (in inches) of a plant at the end
of four weeks.
a. Find the missing values in the ANOVA table. (Round your answer to 2 decimal places.)
ANOVA
Source of Variation
Rows
df
SS
0.13
MS
MSB =
F
FFactor B =
FFactor A =
p-value
0.8182
F crit @ 5%
5.143
2
Columns
44.25
3
MSA =
0.0001
4.757
Error
1.88
6
MSE =
Total
46.26
11
b. At the 5% significance level, can you conclude that average growth of the plant differs by organic
fertilizer?
Yes, since the p-value for Factor A is less than a.
Yes, since the p-value for Factor A is greater than a.
No, since the p-value for Factor A is less than a.
No, since the p-value for Factor A is greater than a.
c. At the 5% significance level, can you conclude that the average growth of the plant differs by acidity
level?
Yes, since the p-value for Factor B is less than a.
Yes, since the p-value for Factor B is greater than a.
No, since the p-value for Factor B is less than a.
No, since the p-value for Factor B is greater than a.
4.
value:
2.50 points
(Round all intermediate calculations to at least 4 decimal places.)
Do energy bills vary dramatically depending on where you live in the United States? Suppose 25
households from four regions in the United States are sampled. The values for the average annual energy
bill are shown below and are consistent with those found by The Department of Energy (Money, June
2009). Use Table 5.
Region
Average annual
Energy bill
West
$1,491
Northeast
$2,319
Midwest
$1,768
South
$1,758
A portion of the ANOVA calculations are below:
ANOVA
Source of Variation
Between Groups
Within Groups
SS
7531769
3492385
df
3
96
MS
?
?
F
?
p-value
7.13E-24
Total
11024154
99
a. Complete the ANOVA table. (Round your answers to 2 decimal places.)
df
MS
F
ANOVA
Source of Variation
Between Groups
Within Groups
SS
7531769
p-value
7.13E-24
3
3492385
96
Total
11024154
99
3.
value:
2.50 points
(Round all intermediate calculations to at least 4 decimal places.)
The following statistics are computed by sampling from three normal populations whose variances are
equal: Use Table 2 and Table 5.
X1 = 22.6, n1 = 6;
X2 = 30.1, n2 = 8;
X3 = 34.0, n3 = 5;
MSE = 28.7
a. Use Fisher's LSD test to determine which population means differ at 95% confidence intervals.
(Negative values should be indicated by a minus sign. Round your answers to 2 decimal places.)
Population Mean
Differences
P1 P2
Confidence Interval
[
[
]
]
Can we conclude that the
population means differ?
(Click to select)
(Click to select) 4
(Click to select) 4
1-M3
9
23
[
]
b. Repeat the analysis with Tukey's HSD approach. (If the exact value for nt - c is not found in the
table, use the value which is closer. Negative values should be indicated by a minus sign. Round
your answers to 2 decimal places.)
Population Mean
Differences
1 - 2
Confidence Interval
]
]
Can we conclude that the
population means differ?
(Click to select)
(Click to select)
(Click to select)
13
12 - 3
[
c. Which of these two approaches would you use to determine whether differences exist between the
population means?
Tukey's HSD
Fisher's LSD
5.
value:
2.50 points
(Round all intermediate calculations to at least 4 decimal places.)
The following observations were obtained when conducting a two-way ANOVA experiment with no
interaction. Use Table 4
Click here for the Excel Data File
Factor B
1
2
3
Xi for Factor A
1
3
8
12
7.667
Factor A
2
3
4
3
10
9
16
14
10.000
8.667
4
5
8.
13
8.667
Xj for Factor B
3.750
8.750
13.750
X = 8.750
a. Calculate SST, SSA, SSB, and SSE. (Round your answers to 2 decimal places.)
,SST
SSA
SSB
SSE
b. Calculate MSA, MSB, and MSE. (Round your answers to 2 decimal places.)
MSA
MSB
MSE