MATH533 week 8 final exam set 2

Week
8 : Final Exam – Final Exam

Page: 1 2
3

Page 1

1.(TCO A)Seventeen salespeople reported the
following number of sales calls completed last month.

72
93
82
81
82
97
102
107 119
86
88
91
83
93
73
100
102

a. Compute the mean, median, mode, and standard
deviation, Q1, Q3, Min, and Max for the above
sample data on number of sales calls per month.
b. In the context of this situation, interpret the Median, Q1,
and Q3. (Points : 33)

2.(TCO B) Cedar Home Furnishings has collected data on
their customers in terms of whether they reside in an urban location or a
suburban location, as well as rating the customers as either “good,”
“borderline,” or “poor.” The data is below.

Urban

Suburban

Total

Good

60

168

228

Borderline

36

72

108

Poor

24

40

64

Total

120

280

400

If
you choose a customer at random, then find the probability that the
customer

a. is considered “borderline.”b. is
considered “good” and resides in an urban location.c. is
suburban, given that customer is considered “poor.” (Points : 18)

3.
(TCO B) Historically, 70% of your customers at Rodale Emporium pay for
their purchases using credit cards. In a sample of 20 customers, find the
probability that

a. exactly 14 customers will pay for their purchases using credit cards.

4.
(TCO B) The demand for gasoline at a local service station is normally
distributed with a mean of 27,009 gallons per day and a standard deviation
of 4,530 gallons per day.

a. Find the probability that the demand for gasoline exceeds 22,000 gallons
for a given day.

b. Find the probability that the demand for gasoline falls between 20,000
and 23,000 gallons for a given day.

c.
How many gallons of gasoline should be on hand at the beginning of each day
so that we can meet the demand 90% of the time (i.e., the station stands a
10% chance of running out of gasoline for that day)? (Points : 18)

5.
(TCO C) An operations analyst from an airline company has been asked to
develop a fairly accurate estimate of the mean refueling and baggage
handling time at a foreign airport. A random sample of 36 refueling and
baggage handling times yields the following results.

Sample Size = 36
Sample Mean = 24.2 minutes
Sample Standard Deviation = 4.2 minutes

a. Compute the 90% confidence interval for the population mean refueling
and baggage time.

b. Interpret this interval.
c.
How many refueling and baggage handling times should be sampled so that we
may construct a 90% confidence interval with a sampling error of .5 minutes
for the population mean refueling and baggage time? (Points : 18)

6.
(TCO C) The manufacturer of a certain brand of toothpaste claims that a
high percentage of dentists recommend the use of their toothpaste. A random
sample of 400 dentists results in 310 recommending their toothpaste.

a. Compute the 99% confidence interval for the population proportion of
dentists who recommend the use of this toothpaste.

b. Interpret this confidence interval.

c. How large a sample size will need to be selected if we wish to have a
99% confidence interval that is accurate to within 3%? (Points : 18)

7.
(TCO D) A Ford Motor Company quality improvement team believes that its
recently implemented defect reduction program has reduced the proportion of
paint defects. Prior to the implementation of the program, the proportion
of paint defects was .03 and had been stationary for the past 6 months.
Ford selects a random sample of 2,000 cars built after the implementation
of the defect reduction program. There were 45 cars with paint defects in
that sample. Does the sample data provide evidence to conclude that the
proportion of paint defects is now less than .03 (with a = .01)? Use the
hypothesis testing procedure outlined below.

a. Formulate the null and alternative hypotheses.

b. State the level of significance.

c. Find the critical value (or values), and clearly show the rejection and
nonrejection regions.

d. Compute the test statistic.

e. Decide whether you can reject Ho and accept Ha or not.

f. Explain and interpret your conclusion in part e. What does this
mean?

g. Determine the observed p-value for the hypothesis test and interpret
this value. What does this mean?

h. Does the sample data provide evidence to conclude that the proportion of
paint defects is now less than .03 (with a = .01)? (Points : 24)

8.
(TCO D) A new car dealer calculates that the dealership must average more
than 4.5% profit on sales of new cars. A random sample of 81 cars gives the
following result.

Sample Size = 81
Sample Mean = 4.97%
Sample Standard Deviation = 1.8%

Does the sample data provide evidence to conclude that the dealership
averages more than 4.5% profit on sales of new cars (using a = .10)? Use
the hypothesis testing procedure outlined below.

a. Formulate the null and alternative hypotheses.

b. State the level of significance.

c. Find the critical value (or values), and clearly show the rejection and
nonrejection regions.

d. Compute the test statistic.

e.
Decide whether you can reject Ho and accept Ha or not.

f. Explain and interpret your conclusion in part e. What does this mean?

g. Determine the observed p-value for the hypothesis test and interpret
this value. What does this mean?

h. Does the sample data provide evidence to conclude that the dealership
averages more than 4.5% profit on sales of new cars (using a = .10)?
(Points : 24)

Page: 1 2
3

Loading
[MathJax]/jax/output/HTML-CSS/fonts/TeX/fontdata.js
Week
8 : Final Exam – Final Exam

Page: 1
2
3

Page 2

1.
(TCO E) Bill McFarland is a real estate broker who specializes in selling
farmland in a large western state. Because Bill advises many of his clients
about pricing their land, he is interested in developing a pricing formula
of some type. He feels he could increase his business significantly if he
could accurately determine the value of a farmer’s land. A geologist tells
Bill that the soil and rock characteristics in most of the area that Bill
sells do not vary much. Thus the price of land should depend greatly on
acreage. Bill selects a sample of 30 plots recently sold. The data is found
below (in Minitab), where X=Acreage and Y=Price ($1,000s).

PRICE

ACREAGE

PREDICT

60

20.0

50

130

40.5

250

25

10.2

300

100.0

85

30.0

182

56.5

115

41.0

24

10.0

60

18.5

92

30.0

77

25.6

122

42.0

41

14.0

200

70.0

42

13.0

60

21.6

20

6.5

145

45.0

61

19.2

235

80.0

250

90.0

278

95.0

118

41.0

46

14.0

69

22.0

220

81.5

235

78.0

50

16.0

25

10.0

290

100.0

.jpg”>

Correlations:
PRICE, ACREAGE

Pearson correlation of PRICE and ACREAGE = 0.997
P-Value = 0.000

Regression
Analysis: PRICE versus ACREAGE

The regression equation is
PRICE = 2.26 + 2.89 ACREAGE

Predictor Coef SE
Coef T P
Constant 2.257
2.231 1.01 0.320
ACREAGE 2.89202
0.04353 66.44 0.000

S = 7.21461 R-Sq =
99.4% R-Sq(adj) = 99.3%

Analysis of Variance

Source
DF SS
MS
F P
Regression 1 229757 229757 4414.11 0.000
Residual
Error 28 1457 52
Total
29 231215

Predicted Values for New Observations

New Obs Fit SE
Fit 95%
CI 95% PI

1 146.86 1.37 (144.05,
149.66) (131.82, 161.90)

2 725.26 9.18 (706.46,
744.06) (701.35, 749.17)XX

XX denotes a point that is an extreme outlier in the
predictors.

Values of Predictors for New Observations

New Obs ACREAGE

1 50

2 250

a.
Analyze the above output to determine the regression equation.

b. Find and interpret in the context of this problem.

c. Find and interpret the coefficient of determination (r-squared).

d. Find and interpret coefficient of correlation.

e. Does the data provide significant evidence (a= .05) that the acreage can be used to predict the
price? Test the utility of this model using a two-tailed test. Find the
observed p-value and interpret.

f. Find the 95% confidence interval for mean price of plots of farmland
that are 50 acres. Interpret this interval.

g. Find the 95% prediction interval for the price of a
single plot of farmland that is 50 acres. Interpret this interval.

h. What can we say about the price for a plot of farmland that is 250
acres? (Points : 48)

Page: 1
2
3

Loading
[MathJax]/jax/output/HTML-CSS/fonts/TeX/fontdata.js
Week
8 : Final Exam – Final Exam

Page: 1
2
3

4

1.(TCO E)An insurance
firm wishes to study the relationship between driving experience (X1, in
years), number of driving violations in the past three years (X2), and
current monthly auto insurance premium (Y). A sample of 12 insured
drivers is selected at random. The data is given below (in MINITAB):

Y

X1

X2

Predict X1

Predict X2

74

5

2

8

1

38

14

0

50

6

1

63

10

3

97

4

6

55

8

2

57

11

3

43

16

1

99

3

5

46

9

1

35

19

0

60

13

3

Regression
Analysis: Y versus X1, X2

The regression equation is
Y = 55.1 – 1.37 X1 + 8.05 X2

Predictor Coef SE
Coef T P
Constant 55.138
7.309 7.54 0.000
X1
-1.3736 0.4885 -2.81 0.020
X2
8.053 1.307 6.16 0.000

S = 6.07296 R-Sq = 93.1%
R-Sq(adj) = 91.6%

Analysis of Variance

Source
DF SS
MS F P
Regression 2
4490.3 2245.2 60.88 0.000
Residual Error 9
331.9 36.9
Total
11 4822.3

Predicted Values for New Observations

New Obs Fit SE
Fit 95%
CI 95% PI
1
52.20 2.91 (45.62, 58.79) (36.97, 67.44)

Values of Predictors for New Observations

New Obs X1 X2
1 8.00 1.00

Correlations:
Y, X1, X2

Y X1
X1 -0.800
0.002

X2 0.933 -0.660
0.000 0.020

Cell Contents: Pearson correlation

P-Value

a. Analyze the above output to determine the multiple regression equation.

b. Find and interpret the multiple index of determination (R-Sq).

c. Perform the t-tests on and on
(use two tailed test with (a=
.05). Interpret your results.

d. Predict the monthly premium for an individual
having 8 years of driving experience and 1 driving violation during the
past 3 years. Use both a point estimate and the appropriate interval
estimate.
(Points : 31)