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# Math 533 Final Essay

1887 words - 8 pages

MATH/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

Ans. b.
H0 must always have equal sign, < 36 weeks

2. (TCO B) The Republican party is interested in studying the number of republicans that might vote in a particular congressional ...view middle of the document...

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

|
Ans.
a.  Range = maximum - minimum
Maximum observation in the data = 67
Minimum observation in the data = 19
range = 67 - 19 =48 sales/ month (Millions \$)
b.  Median
Arrange the data in the ascending order
That is 19, 23, 23, 34, 34, 34, 45, 45, 54, 56, 56 67
Here, sample size n = 12 (even)
So median is the average of two middle observation
Mid=(34+45)/2 = 39.5 sales/month Millions (\$)
c.  From the Mega stat output we have sample standard deviation as s=15.39
Therefore, the range of the data that would contain 68% of the result
That is R +- s
(48-15.39, 48+15.39)
(32.61, 63.39)

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

count 12
mean 34.75
sample variance 146.20
sample standard deviation 12.09
minimum 19
maximum 56
range 37

Stem and Leaf plot for # 1
stem unit = 10
leaf unit = 1

count | 12.00000 |
mean | 34.75000 |
sample variance | 146.20455 |
sample standard deviation | 12.09151 |
minimum | 19.00000 |
maximum | 56.00000 |
range | 37.00000 |
| |
1st quartile | 23.00000 |
median | 34.50000 |
3rd quartile | 45.25000 |
interquartile range | 22.25000 |
mode | 19.00000 |

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)

To construct 95% confidence interval for the data from the Chris Cross Manufacturing, the margin of error is:
E= zc (standard deviation divided by square root of n)
In this case,
zc= z alpha divided by 2 = z 0.05/2 = z 0.025 = 1.96
(1-confidence level)/2
(1-.95)/2
.05/2=.025
looking at z table, Table A.3 Cumulative Areas under the Standard Normal Curve, is -1.96, that is 1.96
...

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