Statistics Help

26 Jun Statistics Help

Applied Business Statistics

1. By looking at a graph of the data, the human resources department has identified a relationship between the amount of training time and the subsequent performance of employees. Which basic activity of statistics is involved? (3 pts)

2. What is involved in the design phase of a statistical study? (3 pts)

3. Use the following to answer questions: World University has published data about undergraduate enrollments in their view book for prospective applicants: (6 pts)

Year

Total Applicants

Accepted

Wait Listed

1992

10,276

1,450

275

1993

11,141

1,500

250

1994

12,077

1,475

250

1995

13,396

1,460

225

1996

13,558

1,450

200

1997

14,122

1,450

175

1998

14,733

1,450

150

1999

15,006

1,425

100

2000

15,891

1,425

50

2001

16,728

1,425

50

a. What is an elementary unit for this data set?

b. What kind of data set is this e.g. univariate?

c. Is this cross-sectional or time-series data?

d. Which of these variables are qualitative? For each, identify whether it is nominal or ordinal.

e. Which of these variables are quantitative? For each, identify whether it is continuous or discrete?

4. An automotive engineer is interested in studying the performance of compact cars from different manufacturers. (6 points)

 

Horsepower	Miles per gallon	Number of Cylinders	Weight	Country origin
100	19.7	8	3365	United States
150	16.9	8	4360	Germany
140	15.5	6	4054	United States
75	36.4	4	1980	Japan
90	22.6	4	2800	Japan

a. What is the elementary unit for this data set?

b. What kind of data set is this?

c. Which of these variables are quantitative? Identify which are continuous or discrete.

d. Which of these variables are qualitative? For each, identify whether it is nominal or ordinal.

e. Is this cross-sectional or time series data?

5. Use the following to answer questions: Refer to the following data set that represents the sales last week of a group of employees of Meriden Marketing Inc. (6 pts)

23

14

26

42

28

21

34

45

32

32

24

34

22

25

22

17

60

f. Draw a stem-and-leaf histogram.

g. Describe the data set represented by the stem and leaf diagram produced for the previous question.

h. Are their any outliers?

i. Draw a histogram.

j. Describe the date set represented by the histogram.

6. Use the following to answer questions: Use the following data set on the 2001 enrollments of a sample of independent colleges in the State of California. (6 pts)

1491	2570	3631	4695	8096	2089	8511	6310	10736	5012
4388	16525	25842	3631	5755	5494	1363	1762	2848	3221

a. Construct a histogram for this data set.

b. Describe the shape of this histogram.

c. Find the logarithm of each data value.

d. Construct a histogram for the data set of logarithms.

e. Describe the shape of this histogram of the logarithms.

7. A professor who teaches class that includes 34 students (in a lecture hall with 34 chairs) gives the first midterm. As each student hands in their exam and leaves the room, the professor records how many minutes it took the student to complete the exam. The professor thus records, in minutes, the amount of time they take to complete the test. (6 points)

 

Time	Frequency
52	2
51	0
50	2
49	1
48	8
47	2
46	1
45	7
44	3
43	2
42	3
41	1
40	1
39	1

 

a.       How long does it take the “typical” student to finish the midterm?

b.      What is the average time spent completing the exam?

c.       Calculate the five number summary

d.      Construct a box plot for the dataset.

e.       Is the data skewed?

f.        Identify any outliers

8. Use the following to answer questions: Your financial analyst gives you the following summary statistics on sales of your major product line: (6 pts)

Maximum

$25,000

Minimum

$17,500

Mean

$20,210

Median

$19,770

First Quartile

$18,750

Third Quartile

$21,500

Mode

$22,000

a. Provide the five number summary for product line sales.

b. Find the amount which 75 percent of all sales exceed.

c. Find the amount which 25 percent of all sales exceed.

d. Is the data set skewed? Why or why not?

9. What does the standard deviation measure? (4 pts)

10. Use the following to answer questions: Janice Jones is Coordinator for Volunteer Services at Parkview Senior Center. She is reviewing data on volunteer hours for last month in the table below: (8 pts)

Volunteer	Total Hours
A	11
B	15
C	23
D	29
E	19
F	22
G	21
H	20
I	15
J	25
K	17

a. Compute the range for volunteer hours.

b. Compute the standard deviation for volunteer hours.

c. Compute the variance for volunteer hours.

d. Find the average for volunteer hours.

e. What percentage of the volunteers works within one standard deviation of the average?

11. Use the following to answer questions: Below is the data on the cost, in cents, of a random sample of candy bars: (12 pts)

30

40

40

55

50

45

40

70

35

110

40

60

40

45

a. Find the average.

b. Find the standard deviation.

c. Interpret the standard deviation.

d. Find the range. What are the units of measurement?

e. Find the coefficient of variation.

f. Find the variance.

g. Delete the outlier. Calculate the standard deviation.

h. All candy bar prices are to be raised by 10 cents. What will the average, standard deviation, range, and coefficient of variation be now?

12. Use the following to answer questions: Sarah Fernandez, Manager of Operations, is analyzing employee absenteeism at the San Diego Assembly Plant. Ten percent of all plant employees work in the finishing department, 20% of all plant employees are absent excessively; and 7% of all plant employees work in the finishing department and are absent excessively. (10 pts)

a. Draw the probability tree.

b. Find the probability that an employee selected at random works in the finishing department.

c. Find the probability that an employee selected at random works in the finishing department and is absent excessively.

d. Given that the employee selected at random works in the finishing department, find the probability that the employee is absent excessively.

e. Are the events “working in the finishing department” and “absent excessively” mutually exclusive?

f. Are the events “working in the finishing department” and “absent excessively” independent?

13. Use the following to answer questions: The internal audit group of Suburban Civic Bank has found that 10% of all personal loans are in default. Homeowners represent 20% of the loans in default and 70% of the loans that are not in default. (8 pts)

a. Draw the probability tree.

b. If a personal loan is selected at random, find the probability that it is to a homeowner and is not in default.

c. If a personal loan is selected at random is to a homeowner, find the probability that the loan is in default.

d. If a personal loan is selected at random, find the probability that the loan is not in default.

e. Are the events “homeowner” and “loan in default” mutually exclusive?

f. Are the events “homeowner” and “loan not in default” independent?

14. Use the following to answer questions: The table below presents the probability distribution for X = the number of email messages you will receive in the next 10 minutes. (8 pts)

X	0	1	2	3
P(X)	.35	.35	.25	.05

a. What is the probability that no emails will be received?

b. What is the probability that at least one email will be received?

c. What is E(X), the expected number of emails that will be received?

d. What is Var(X), the variance of the number of emails that will be received?

e. What is the Std(X), the standard deviation of the number of emails that will be received?

15. Site preparation for new housing developments for tracts of 50 houses are normally distributed with a mean of 200 and a standard deviation of 10 workdays. (8 points)

a. Find the probability that the site is completed within 185 workdays

b. Find the probability that the site will not be completed within 215 workdays

c. EXTRA CREDIT (4 pts) Find the probability that the site is completed between 185 and 215 days.

EXTRA CREDIT: Draw a positively skewed distribution, negatively skewed distribution, and a normal distribution and indicate on each approximately where the mean, median, and mode would fall. (5 points)