# Gm 533 applied managerial statistics final_exam complete answer

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Set 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.

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.”

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.
b. at least 10 customers will pay for their purchases using credit cards.
c. at most 12 customers will pay for their purchases using credit cards. (Points : 18)

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)?

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?

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%?

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 = .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 = .01)?

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  = .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  = .10)?

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

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 (= .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?

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 (= .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.

Set 2

1. (TCO D) PuttingPeople2Work has a growing business placing out-of-work MBAs. They claim they can place a client in a job in their field in less than 36 weeks. You are given the following data from a sample.
Sample size: 100
Population standard deviation: 5
Sample mean: 34.2
Formulate a hypothesis test to evaluate the claim. (Points : 10)
Ho: µ = 36; Ha: µ ≠ 36
Ho: µ ≥ 36; Ha: µ < 36
Ho: µ ≤ 34.2; Ha: µ > 34.2
Ho: µ > 36; Ha: µ ≤ 36

2. (TCO B) The Republican party is interested in studying the number of republicans that might vote in a particular congressional district. Assume that the number of voters is binomially distributed by party affiliation (either republican or not republican). If 10 people show up at the polls, determine the following:

Binomial distribution

10 n
0.5 p

X P(X) cumulative
probability
0 0.00098 0.00098
1 0.00977 0.01074
2 0.04395 0.05469
3 0.11719 0.17188
4 0.20508 0.37695
5 0.24609 0.62305
6 0.20508 0.82813
7 0.11719 0.94531
8 0.04395 0.98926
9 0.00977 0.99902
10 0.00098 1.00000

What is the probability that no more than four will be republicans? (Points : 10)
38%
12%
21%
62%

3. (TCO A) Company ABC had sales per month as listed below. Using the Minitab output given, determine:
(A) Range (5 points);
(B) Median (5 points); and
(C) The range of the data that would contain 68% of the results. (5 points).
Raw data: sales/month (Millions of \$)
23
45
34
34
56
67
54
34
45
56
23
19

Descriptive Statistics: Sales
Variable Total Count Mean StDev Variance Minimum Maximum Range
Sales 12 40.83 15.39 236.88 19.00 67.00 48.00

Stem-and-Leaf Display: Sales
Stem-and-leaf of Sales N = 12
Leaf Unit = 1.0
1 1 9
3 2 33
3 2
6 3 444
6 3
6 4
6 4 55
4 5 4
3 5 66
1 6
1 6 7

Reference:
(TCO A) Company ABC had sales per month as listed below. Using the MegaStat output given, determine:
(A) Range (5 points)
(B) Median (5 points)
(C) The range of the data that would contain 68% of the results. (5 points)

Raw data: sales/month (Millions of \$)
19
34
23
34
56
45
35
36
46
47
19
23

4. (TCO C, D) Tesla Motors needs to buy axles for their new car. They are considering using Chris Cross Manufacturing as a vendor. Tesla’s requirement is that 95% of the axles are 100 cm ± 2 cm. The following data is from a test run from Chris Cross Manufacturing. Should Tesla select them as a vendor? Explain your answer.

Descriptive statistics

count 16
mean 99.850
sample variance 4.627
sample standard deviation 2.151
minimum 96.9
maximum 104
range 7.1
population variance 4.338
population standard deviation 2.083
standard error of the mean 0.538
tolerance interval 95.45% lower 95.548
tolerance interval 95.45% upper 104.152
margin of error 4.302
1st quartile 98.850
median 99.200
3rd quartile 100.550
interquartile range 1.700
mode 103.000
(Points : 25)

5. (TCO D) A PC manufacturer claims that no more than 2% of their machines are defective. In a random sample of 100 machines, it is found that 4.5% are defective. The manufacturer claims this is a fluke of the sample. At a .02 level of significance, test the manufacturer’s claim, and explain your answer.

Test and CI for One Proportion
Test of p = 0.02 vs p > 0.02

Sample X N Sample p 98% Lower Bound Z-Value P-Value
1 4 100 0.040000 0.000000 1.43 0.077

Finals page 2
1. (TCO B) The following table gives the number of visits to recreational facilities by kind and geographical region.
(Points : 30)

finals 2 -2
2. (TCO B, F) The length of time Americans exercise each week is normally distributed with a mean of 15.8 minutes and a standard deviation of 2.2 minutes

X P(X≤x) P(X≥x) Mean Std dev
11 .0146 .9854 15.8 2.2
15 .3581 .6419 15.8 2.2
21 .9910 .0090 15.8 2.2
24 .9999 .0001 15.8 2.2
p(lower) p(upper)

(A) Analyze the output above to determine what percentage of Americans will exercise between 11 and 21 minutes per week. (15 points)
(B) What percentage of Americans will exercise less than 15 minutes? If 1000 Americans were evaluated, how many would you expect to have exercised less than 15 minutes? (15 points) (Points : 30)

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