Stats for Strategy Exam 3 In-Class Practice Questions • Choose the

Stats for Strategy Exam 3
In-Class Practice Questions
• Choose the single best answer. Work together with classmates. Check answers with TAs.
• Jump to Notebook Topics when a question puzzles! (Use for review as well as practice.)
• Use formula sheet in Notebook. Exam 3 Additional Practice Questions are posted online.
Disclaimer: These practice questions familiarize you with the style of the exam but actual exam
questions cover different content. Practice questions don’t replace homework; they only add value.
Questions 1–3.
1. In a study of 2015 model cars, a researcher found that 64% of the variation in the price of
cars is explained by the least-squares regression on the car’s engine horsepower. For the cars
in this study, cars with less horsepower tended to have lower prices. The correlation is
(a) −0.80
(b) 0.36
(c) 0.4096
(d) 0.64
(e) None of the answers is correct
2. In the Tippie College, the dean responsible for scheduling classes notices that demand is low
for classes meeting before 10:00 AM or after 3:00 PM and is high for classes meeting between
10:00 AM and 3:00 PM. We may conclude which of the following?
(a) There is an association between demand for classes and the times classes meet.
(b) There is a positive association between demand for classes and the times classes meet.
(c) There is a negative association between demand for classes and the times classes meet.
(d) There is no association between demand for classes and the times classes meet.
3. The stores of a large retail chain were divided into three groups. While customers were
shopping, Group 1 played pop music, Group 2 played classical music, and Group 3 played
hip-hop music. Daily sales were recorded in each store for 30 days. Suppose that, on average,
sales were highest in those stores which played pop music, second highest for those stores
playing hip-hop, and lowest for stores playing classical music. We conclude:
(a) There is a positive association between sales and type of music played.
(b) There is a negative association between sales and type of music played.
(c) There is both positive and negative association between sales and type of music played.
(d) None of the above
1
Questions 4–10.
An Iowa City realtor believes that the current value of homes in a certain historic neighborhood in
Iowa City is positively associated with the age of the homes— that is, she believes that older homes
tend to be worth more because the historic construction and ambience appeal to home buyers. Data
from a random sample of 10 homes from the neighborhood which were sold recently are shown in
the table. MINITAB graphs and some regression output are shown below.
Sales Price (dollars)
126000
142000
107500
110000
94000
Age (years)
39
40
45
42
43
Sales Price (dollars)
99500
78000
55790
70000
53600
Fitted Line Plot
Age (years)
24
68
79
80
62
Residuals vs. Fitted Values
Sales Price = 155115 - 1178 Age
(response is Sales Price)
S
140000
130000
40000
20270.5
R-Sq
57.4%
R-Sq(adj)
52.1%
30000
20000
110000
Residual
Sales Price
120000
100000
90000
80000
10000
0
-10000
70000
-20000
60000
-30000
50000
20
30
40
50
60
70
80
60000
Age
Analysis of Variance
Source
DF
Adj SS
Regression
1 4432200791
Age
1 4432200791
Error
8 3287160099
Total
9 7719360890
Model Summary
S
R-sq
20270.5 57.42%
R-sq(adj)
52.09%
Coefficients
Term
Coef
Constant 155115
Age
-1178
SE Coef
19785
359
Adj MS
4432200791
4432200791
410895012
F-Value
10.79
10.79
P-Value
0.011
0.011
R-sq(pred)
31.13%
T-Value
7.84
-3.28
P-Value
0.000
0.011
VIF
1.00
Prediction for Sales Price
Fit
84453.0
80000
90000
100000
Fitted Value
Regression Analysis: Sales Price versus Age
Variable
Age
70000
Setting
60
SE Fit
6993.74
95% CI
(68325.4, 100581)
95% PI
(35005.0, 133901)
2
110000
120000
130000
4. Identify the hypotheses to test the realtor’s belief.
(a) H0 : β1 > 0
(b) HA : β1 ̸= 0
(c) HA : β1 > 0
(d) H0 : β1 < 0
HA : β1 ≤ 0
H0 : β1 = 0
H0 : β1 ≤ 0
HA : β1 ≥ 0
(e) None of the answers is correct
5. What’s the P -value for testing the realtor’s belief?
(a) 0.000
(b) 0.0055
(c) 0.011
(d) 0.022
(e) None of the answers is correct
6. What’s the decision for the hypothesis test of the realtor’s belief at a 2% significance level?
(a) Reject H0
(b) Fail to Reject H0
(c) Cannot be determined based on the available information
7. What’s the English interpretation for the hypothesis test of the realtor’s belief?
(a)
(b)
(c)
(d)
(e)
There is not sufficient evidence to show that mean sales price is positively related to age.
There is sufficient evidence to show that mean sales price is positively related to age.
There is not sufficient evidence to show that mean sales price is negatively related to age.
There is sufficient evidence to show that mean sales price is negatively related to age.
Cannot be determined based on the available information
8. Calculate a 90% confidence interval for the slope β1 .
(a)
(b)
(c)
(d)
(e)
(−1827.5, −527.9)
(−1844.7, −510.7)
(−1976.7, −378.7)
(−2004.6, −350.8)
None of the answers is correct to the first decimal place
9. Estimate with 95% certainty the sales price for a 60-year-old home in the neighborhood.
(a)
(b)
(c)
(d)
(e)
($0 , $100,581)
($35,005 , $133,901)
($0 , $133,901)
($68,325 , $100,581)
Cannot be determined based on the available information
10. Estimate with 95% certainty the mean sales price of all 60-year-old homes in the neighborhood.
(a)
(b)
(c)
(d)
(e)
($0 , $100,581)
($35,005 , $133,901)
($0 , $133,901)
($68,325 , $100,581)
Cannot be determined based on the available information
(next page blank)
3
4
Questions 11–12.
Consider the partial MINITAB output for the regression of a predictor variable x on a response
variable y. (Some items are missing!)
The regression equation is
Y = 349 + 0.590 X
Predictor
Constant
X
Coef
349.38
0.5905
SE Coef
18.10
0.2070
T
19.31
2.85
P
0.000
0.006
MS
55034
6762
F
8.14
Analysis of Variance
Source
Regression
Residual Error
Total
DF
1
57
58
SS
55034
385454
440488
P
0.006
11. What percentage of the variation in y is explained by variation in x along the regression line?
(a) 0.6%
(b) 12.5%
(c) 18.1%
(d) 20.7%
(e) None of the answers is correct to the first decimal place
12. Find the best estimate of the population standard deviation σ common to all bell curves on
the theoretical (population) regression line.
(a) 0.21
(b) 8.14
(c) 18.10
(d) 82.23
(e) None of the answers is correct to the second decimal place
5
Questions 13–17.
A sample of 30 recently-sold single-family homes in a small city is available for study.
We wish to predict y = sales price (in thousands of dollars.) We have information about
x1 = assessed value (in thousands of dollars) and x2 = elapsed time between assessment and sale
(in months.) Notice that the actual sales price and the assessed value often differ dramatically!
The data are shown below.
Home
1
2
3
4
5
..
.
Sales Price
94.10
101.90
88.65
115.50
87.50
..
.
Assessed Value
65.54
72.43
85.61
60.80
81.88
..
.
Elapsed Time
10
10
11
2
5
..
.
30
95.90
79.07
12
Refer to MINITAB output and graphs on the following pages. Choose the best conservative model,
according to the principles which we discussed in class and using 5% significance. Use this model
to answer the following questions.
13. Interpret β1 .
(a) Mean sales price increases by $1780 for every $1000 increase in assessed value, when
time since assessment is held constant.
(b) Mean sales price is not related to assessed value, after accounting for time since assessment.
(c) Mean sales price increases by $1750 for every $1000 increase in assessed value, when
time since assessment is held constant.
(d) Mean sales price increases by $1780 for every $1000 increase in assessed value.
(e) Mean sales price increases by $1750 for every $1000 increase in assessed value.
14. Interpret β2 .
(a) Sales prices for homes with the same assessed value increase by $368 for each extra
month since assessment, on average.
(b) The mean sales price increases by $698 for each extra month since assessment, when
assessed value is held constant.
(c) The mean sales price is unrelated to time since assessment, after accounting for assessed
value.
(d) The mean sales price increases by $368 for each extra month since assessment.
(e) The mean sales price increases by $698 for each extra month since assessment.
(continued)
6
15. Estimate with 95% certainty the sales price for a home which has an assessed value of $70,000
and which sells 12 months after assessment.
(a) ($67,724 , $82,681)
(b) ($68,835 , $120,628)
(c) ($69,955 , $83,480)
(d) ($74,401 , $79,034)
(e) None of the answers is correct to the nearest dollar
16. Estimate with 95% certainty the mean sales price for all homes whose assessed value is $70,000
and which sell 12 months after assessment.
(a) ($74,401 , $79,034)
(b) ($69,955 , $83,480)
(c) ($88,990 , $100,470)
(d) ($72,908 , $77,497)
(e) None of the answers is correct to the nearest dollar
17. What percentage of the variation in sales price is explained by the predictor variable or
variables?
(a) 6.4%
(b) 92.6%
(c) 93.9%
(d) 94.3%
(e) None of the answers is correct to the first decimal place
(MINITAB output and graphs begin next page)
7
Model 1
Analysis of Variance
Source
Regression
Assessed Value
Error
Total
DF
1
1
28
29
Model Summary
S
R-sq
3.47493 92.56%
Coefficients
Term
Constant
Assessed Value
Adj SS
4206.7
4206.7
338.1
4544.8
R-sq(adj)
92.29%
Coef
-44.17
1.7817
Adj MS
4206.67
4206.67
12.08
F-Value
348.37
348.37
P-Value
0.000
0.000
R-sq(pred)
91.15%
SE Coef
7.35
0.0955
T-Value
-6.01
18.66
P-Value
0.000
0.000
VIF
1.00
Regression Equation
Sales Price = -44.17 + 1.7817 Assessed Value
Prediction for Sales Price
Fit
68.0755
75.2024
80.5475
85.8927
SE Fit
1.45080
1.11993
0.898700
0.724641
95% CI
(65.1037, 71.0474)
(72.9083, 77.4965)
(78.7066, 82.3884)
(84.4083, 87.3770)
95% PI
(60.3620, 75.7891)
(67.7238, 82.6810)
(73.1953, 87.8998)
(78.6215, 93.1639)
Model 2
Regression Analysis: Sales Price versus Time
Analysis of Variance
Source
Regression
Time
Error
Lack-of-Fit
Pure Error
Total
DF
1
1
28
12
16
29
Adj SS
289.6
289.6
4255.2
2626.1
1629.1
4544.8
Model Summary
S
R-sq
12.3277 6.37%
R-sq(adj)
3.03%
Coefficients
Term
Coef
Constant 86.36
Time
0.698
SE Coef
4.94
0.506
Adj MS
289.6
289.6
152.0
218.8
101.8
F-Value
1.91
1.91
P-Value
0.178
0.178
2.15
0.077
R-sq(pred)
0.00%
T-Value
17.47
1.38
P-Value
0.000
0.178
VIF
1.00
Regression Equation
Sales Price = 86.36 + 0.698 Time
Prediction for Sales Price
Fit
94.7315
94.7315
94.7315
94.7315
SE Fit
2.80187
2.80187
2.80187
2.80187
95%
(88.9921,
(88.9921,
(88.9921,
(88.9921,
CI
100.471)
100.471)
100.471)
100.471)
95%
(68.8353,
(68.8353,
(68.8353,
(68.8353,
8
PI
120.628)
120.628)
120.628)
120.628)
Model 3
Regression Analysis: Sales Price versus Assessed Value, Time
Analysis of Variance
Source
Regression
Assessed Value
Time
Error
Total
Model Summary
S
R-sq
3.09675 94.30%
Coefficients
Term
Constant
Assessed Value
Time
DF
2
1
1
27
29
Adj SS
4285.85
3996.29
79.18
258.93
4544.78
R-sq(adj)
93.88%
Coef
-44.99
1.7506
0.368
Adj MS
2142.92
3996.29
79.18
9.59
F-Value
223.46
416.72
8.26
P-Value
0.000
0.000
0.008
R-sq(pred)
92.18%
SE Coef
6.55
0.0858
0.128
T-Value
-6.87
20.41
2.87
P-Value
0.000
0.000
0.008
VIF
1.02
1.02
Regression Equation
Sales Price = -44.99 + 1.7506 Assessed Value + 0.368 Time
Prediction for Sales Price
Fit
69.7150
76.7174
81.9692
87.2210
SE Fit
95% CI
95% PI
1.41321 (66.8154, 72.6147) (62.7307, 76.6994)
1.12876 (74.4014, 79.0335) (69.9545, 83.4804)
0.941400 (80.0376, 83.9008) (75.3281, 88.6104)
0.794194 (85.5915, 88.8506) (80.6614, 93.7807)
Residuals from Model 2 vs. Assessed Value
30
5.0
20
Sales Price Residuals
Sales Price Residuals
Residuals from Model 1 vs. Time
7.5
2.5
0.0
-2.5
10
0
-10
-20
-5.0
-30
0
2
4
6
8
10
12
14
16
18
60
Time
65
70
75
Assessed Value
9
80
85
90
Answers
1. e
0.80
2. a
3. d
Sales is quantitative but Type of Music is categorical. The concepts of positive and
negative associations only make sense when both variables are quantitative.
4. c
5. e
P -value= 0.9945
6. b
7. a
8. b
9. b
10. d
11. b
12. d
13. c
14. a
15. e
($75,328 , $88,610)
16. e
($80,038 , $83,901)
17. d
10