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By September 30, 2017Academic Papers
GM 533 Applied Managerial Statistics Final Exam Answers
(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.
(TCO B) Assume that customers patronizing the newly opened Nordstrom’s at River City Mall are binomially distributed by wealth (rich = income greater than $250,000/year; poor = the rest of us). If 10 people visit the Nordstrom’s on a typical weekend shopping day, 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 at least three will be rich?
 3.
Question :
(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: SalesStem-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
 4.
Question :
(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
 5.
Question :
(TCO D) A PC manufacturer claims that no more than 5% of their machines are defective. In a random sample of 100 machines, it is found that 8.5% 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 = 0.05 vs p > 0.05
Sample
X
N
Sample p
98% Lower Bound
Z-Value
P-Value
1
8
100
0.080000
0.024283
1.38
0.084
(TCO B) The following table gives the median incomes of families by level of income and geographical region.
East
South
Midwest
West
Totals
<$80,000/year
102
98
39
62
301
$80,000 to less than $250,000/year
263
514
120
351
1248
$250,000/year or more
100
226
65
99
490
Totals
465
838
224
512
2039
(A) Referring to the above table, if a family is chosen at random, what is the probability that it is either from the South or from the West? (15 points)
(B) Referring to the above table, given that the family is from the Midwest, what is the probability that it has an annual income of at least $250,000? (15 points)
(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
Stddev
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)
 3.
Question :
(TCO C) A random sample of 16 Google managers yields the following information on annual salaries. The sample mean is $89,000, with a sample standard deviation of $8,000. What is the mean salary of all Google managers? What is the 95% confidence interval for the population mean?One-Sample T
N
Mean
StDev
SE Mean
95% CI
16
89000
8000
2000
(84737, 93263)
(TCO E and F) The U.S Department of Transportation and Safety performed an analysis to determine safe driving speeds. To obtain information about the safe driving speed, it analyzed data from multiple countries comparing the maximum allowed speed limit to the observed death rate. The analysis revealed the following:
Refer to the Minitab output below to answer questions A through G.
Regression Equation
Death rate (per 100 million vehicles = -0.535979 + 0.0789418 Speed limit (miles per hour)
Coefficients
Term
Coef
SE Coef
T
P
95% CI
Constant
-0.535979
2.34352
-0.22871
0.825
(-5.94014, 4.86818)
Speed limit (miles per hour)
0.078942
0.03849
2.05106
0.074
(-0.00981, 016770)
Summary of Model
S = 0.836621
R-Sq = 34.46%
R-Sq(adj) = 26.27%
PRESS = 10.8252
R-Sq(pred) = -26.70%
Analysis of Variance
Source
DF
Seq SS
Adj SS
Adj MS
F
Regression
1
2.94453
2.94453
2.94453
4.20687
  Speed limit (miles per hour)
1
2.94453
2.94453
2.94453
4.20687
Error
8
5.59947
5.59947
0.69993
  Lack-of-Fit
3
3.37947
3.37947
1.12649
2.53714
  Pure Error
5
2.22000
2.22000
0.44400
Total
9
8.54400
Source
   P
Regression
0.074385
  Speed limit (miles per hour)
0.074385
Error
  Lack-of-Fit
0.170419
  Pure Error
Total
Predicted Values for New Observations
New Obs
Fit
SE Fit
95% CI
95% PI
1
4.20053
0.265262
(3.58883, 4.81222)
(2.17663, 6.22443)
Values of Predictors for New Observations
New Obs
Speed limit (miles per hour)
1
60
(A) Analyze the above output to determine the regression equation. (10 points)
(B) What conclusions are possible using the meaning of b0 (intercept) and b1 (regression coefficient) in this problem? (That is, explain the meaning of the coefficients.) (10 points)
(C) What conclusions are possible using the coefficient of determination (r-squared)? (6 points)
(D) Calculate the coefficient of correlation. Interpret this value. (6 points)
(E) Does this data provide significant evidence (a=0.05) that the death rate is associated with the speed limit? Find the p-value and interpret. (6 points)
(F) Determine the average death rate for a speed limit of 60 miles per hour. (6 points)
(G) What is the 95% confidence interval for the death rate for a speed limit of 60 miles per hour? What conclusion is possible using this interval? (6 points)
(TCO E and F) A national trade association is concerned with increasing competition from foreign companies. They decide, in close consultation with their membership, to evaluate the sales performance of 25 randomly selected U.S. companies, so that all companies can benefit from their collective experience.
The association’s research director, with substantial input from member companies’ sales managers, has decided to measure the performance, y, of each company by using the yearly sales of the same product for all of the companies.
The research director and the sales managers believe that sales performance, y (measured in hundreds of units), substantially depends on three independent variables:
x1  = sales of the product and all competing products in the company (Market Potential, in hundreds of units)
x2   = dollar advertising expenditures in the company (Advertising, in hundreds of dollars)
x3  = weighted average of the company’s market share over the previous four years (Market Share)
Refer to the Minitab output below to answer questions A through G.
Multiple Regression and Model Building: Minitab Output
Coefficients
Term
Coef
SE Coef
T
P
95% CI
Constant
-1603.58
505.550
-3.17195
0.005
(-2654.93, -552.231)
Market Potential, x1
0.05
0.007
7.26321
0.000
(0.04, 0.070)
Advertising, x2
0.17
0.044
3.78288
0.001
(0.08, 0.260)
Market Share, x3
282.75
48.756
5.79927
0.000
(181.35, 384.139)
Summary of Model
S = 545.515
 R-Sq = 84.90%
R-Sq(adj) = 82.74%
RESS = 8616510
P  R-Sq(pred) = 79.18%
Analysis of Variance
Source
DF
Seq SS
Adj SS
Adj MS
F
P
Regression
3
35130240
35130240
11710080
39.3502
0.0000000
Market Potential, x1
1
14788185
15698916
15698916
52.7542
0.0000004
Advertising, x2
1
10333786
4258521
4258521
14.3102
0.0010905
Market Share, x3
1
10008270
10008270
10008270
33.6315
0.0000093
Error
21
6249309
6249309
297586
Total
24
41379549
Predicted Values for New Observations
New Obs
Fit
SE Fit
95% CI
95% PI
1
4251.56
178.023
(3881.34, 4621.78)
(3058.22, 5444.90)
Values of Predictors for New Observations
New Obs
Marketing Potential, x1
Advertising, x2
Market Share, x3
1
35182.7
7281.65
9.64
  1. Analyze the above output to determine the multiple regression equation. (5 points)
  2. What conclusions are possible using the result of the global usefulness test (the F test and its associated p-value)? (5 points)
  3. What conclusions are possible using the results of the t-tests of the independent variables (alpha = 0.05). Does this data provide significant evidence that Sales are associated with Market Potential and/or Advertising and/or Market Share?  Find the p-values and interpret. Interpret the 95% confidence interval of each of the regression coefficients, using the units of the variables. (20 points)
Find and interpret the 95% Prediction interval for Sales, when Market Potential = 35182.7, Advertising = 7281.65, and Market Share = 9.64. (10 points)
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