**GM 533 Applied Managerial Statistics Final Exam Complete A+ Answer**

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 ≤ 362. (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 pX 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 1.00000What 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

19Descriptive Statistics: Sales

Variable Total Count Mean StDev Variance Minimum Maximum Range

Sales 12 40.83 15.39 236.88 19.00 67.00 48.00Stem-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 7Reference:

(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

234. (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 > 0.02Sample X N Sample p 98% Lower Bound Z-Value P-Value

1 4 100 0.040000 0.000000 1.43 0.077Finals 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 minutesX 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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