MATH533 week 8 final exam set 1

MATH/.blogspot.com/2011/12/gm533-finals.html”>GM 533 Final Exam

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

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

Final
Page 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)