7.569 + 2.023 + 21.218 = 30.81
Standard Deviation: Square root of variance = 5.550675635 or 5.55
Project 3
rp = (.1 * 15) + (.7 * 11) + (.2 * 5)
rp = (1.5) + (7.7) + (1) = 10.20%
Variance:
.1 * (15 – 10.20)² = 2.304
.7 * (11 – 10.20)² = .448
.2 * (5 – 10.20)² = 5.408
2.304 + .448 + 5.408 = 8.16
Standard Deviation: Square root of variance = 2.856571371 or 2.86
Emery, Finnerty & Stowe
Chapter 6. – Risk and Return: Stocks
B6. Rank the projects on the basis of (1) expected return and (2) risk. Which project
would you choose?
Expected return (lowest to highest): 3, 2, 1
Risk (lowest to highest): 1, 3, 2
Project 1 is the best choice, because of its highest expected return and lowest risk.
B10. (Excel: Calculating means, standard deviations, covariance, and correlation)
Given the probability distributions of returns for stock X and stock Y, compute:
B10A.The expected return for each stock, x (mean) and y (mean) and here.
Stock X =
rp = (.2 * 5) + (.2 * 10) + (.4 * 12) + (.15 * 14) + (.05 * 18)
rp = 1 + 2 + 4.8 + 2.1 + .9 = 10.8%
Stock Y =
rp = (.2 * 12) + (.2 * 10) + (.4 * 8) + (.15 * 0) + (.05 * 2)
rp = 2.4 + 2 + 3.2 + 0 + .1 = 7.7%
Cooper & Schlinder Text
Chapter 7. – Sampling Design
5. Your task is to interview a representative sample of attendees for the large concert venue where you work. The new season schedule includes 200 live concerts featuring all types of musicians and musical groups. Since neither the number of attendees nor their descriptive characteristics are known in advance, you decide on nonprobability sampling. Based on past seating configurations, you can calculate the number of tickets that will be available for each of the 200 concerts. Thus, collectively, you will know the number of possible attendees for each type of music. From attendance research conducted at concerts held during the previous two years, you can obtain gender data on attendees by type of music. How would you conduct a reasonably reliable nonprobability sample?
Nonprobability sampling is arbitrary and subjective. Knowing this, the way that I would conduct a reasonably reliable nonprobability sample, is by first selecting the sampling technique and then draw the sample. The sampling technique that I would use is quota sampling, because I have some controls like the number of possible attendees for each type of music, gender data from the attendance of past two years by type of music.
Lind, Marchal, & Wathen Text
Chapter 8. – Sampling Methods and the Central Limit Theorem
31. The Sony Corporation produces a Walkman that requires two AA batteries. The
mean life of these batteries in this product is 35.0 hours. The distribution of the
battery lives closely follows the normal probability distribution with a standard
deviation of 5.5 hours. As a part of their testing program Sony tests samples of 25
batteries.
A. What can you say about the shape of the distribution of sample mean?
The shape of the distribution of the sample mean is a normal probability distribution
B. What is the standard error of the distribution of the sample mean?
Standard error = 5.5/√25 = 1.1. The standard error of the mean is 1.1.
C. What proportion of the samples will have a mean useful life of more than 36 hours?
36 – 35 = 1 = .909 .909 = 0.3389 (from appendix D)
5.5 / √25 1.1 (0.5000 - 0.3389 = .1611)
The probability of a battery lasting more than 36 hours is 16%.
D. What proportion of the sample will have a mean useful life greater than 34.5 hours?
34.5 – 35 = -.5 = -.4545 -.4545 = .1736 (from appendix D)
5.5 / √25 1.1 (0.5000 - .1736 = .3264)
The probability of a mean life greater then 34.5 hours is .3264 or 33%.
Lind, Marchal, & Wathen Text
Chapter 8. – Sampling Methods and the Central Limit Theorem
31. (Continued).
E. What proportion of the sample will have a mean useful life between 34.5 and 36.0 hours?
0.3389 (c) - 0.1736 (d) = 0.1653
The probability is 16% having a mean useful life between 34.5 and 36.
36 – 34.5 / 5.5 / √25 = 1.5/ 1.1 = 1.36
Sevilla & Somers.
Topic 8 – Indexes and Ratings
Exploration 12. The following graph, created using data from the Missouri Economic and Information Center (http://www.misssourieconomy.org) shows the value of the Purchasing Managers’ Index from August 2003 to July 2005.
- Use the Web to find how this index is calculated.
This index is used to forecast the economy of the state of Missouri for the next three to six months. If the score is greater than 50, it indicates the economy is in a growing phase. A score of 49 or below indicates a slow economy. The Missouri Economic and Information Center is responsible for the Purchasing Managers Index (PMI) for the state of Missouri. Missouri is one of two groups of indices that are part of the Mid-American Business Conditions Survey. This survey is performed by Creighton University in Omaha, NE, once a month. This index for the years from 2003 to 2005 had many factors that needed to be considered.
The Purchasing Manager’s Index (PMI) is calculated by the Institute for Supply
Management (ISM). It is a non-profit group consisting of over 40,000 members that
work in the supply management and purchasing fields. The PMI is released the 1st of
each month and consists of raw data by over 400 companies. The PMI consists of 5
sub-indicators which are weighted differently.
They are as follows:
- Production Levels (.25)
- New Orders (.30)
- Supplies Deliveries (.15)
- Inventories (.10)
- Employment Levels (.20)
Sevilla & Somers.
Topic 8 – Indexes and Ratings
- (Continued).
The ISM contacts over 400 companies and asks them a series of questions, in which they can only answer in three ways. The questions are in reflection of the previous month.
They are as follows:
All of the answers that are reported as “better” are equal to 1. All of the answers that
are reported as the “same” are equal to .50. And all answers reported as “worse”
are designated as a 0.
For example, if 50 out of 100 companies report their production levels as “better,” 30
out of 100 report as the “same,” and 20 out of 100 report as “worse;” then the total
points for production levels would be (50+(30*.5)), which is a total of 65 points.
This is done for each “sub-indicator” and the points are weighed accordingly. Thus,
producing the PMI for that month.
Sevilla & Somers.
Topic 8 – Indexes and Ratings
B. Describe what the graph shows in this context.
The graph depicts a sharp decline between August and September of 2003. However, the PMI recovers between September and October of 2003, and manages to stay fairly consistent until February of 2004. At this time the PMI has a steady incline, hitting its highest point in April 2004, which is well of 70. At that point the PMI steadily decreases until June, where it seems to have leveled off in the mid 60’s until November 2004. At this point the PMI increases again in December of 2004. However after this point the trend seems to gradually decrease in 2005, seeming to end in June 2005, at one of the lowest points in the Purchasing Manager’s Index of mid 2003-mid 2005.
Lind, Marchal, & Wathen Text
Chapter 18 – Index Numbers
- Compute a simple price index for each of the four items. Use 2000 as the base period.
To compute the simple price index, take the price for a selected period and divide by the price shown in the base year (Lind, 2005).
2000 2004
Item Price Quantity Price Quantity
Margarine .081 18 0.89 27
(pound)
Shortening 0.84 5 0.94 9
(pound)
Milk 1.44 70 1.42 65
(1/2 gallon)
Potato chips 2.91 27 3.07 33
P = p1 / p0 x 100
Margarine (pound) = P = p2004 / p2000 x 100
P = .89 / .81 x 100 = 109.8765
Shortening (pound) = P = p2004 / p2000 x 100
P = .94 / .84 x 100 = 111.9048
Milk = P = p2004 / p2000 x 100
P = 1.42 / 1.44 x 100 = 98.6111
Potato Chips = P = p2004 / p2000 x 100
P = 3.07 / 2.91 x 100 = 105.4983
Lind, Marchal, & Wathen Text
Chapter 18 – Index Numbers
- Compute a simple aggregate price index. Use 2000 as the base period.
To compute the simple aggregate price index, take the sum of the prices for a selected period and divide by the sum of the price index in the base year (Lind, 2005).
P = (.89 + .94 + 1.42 + 3.07) / (.81 + .84 + 1.44 + 2.91 ) x 100
P = 6.32 / 6.00 x 100
P = 1.0533333 x 100
P = 105.333333
Lind, Marchal, & Wathen Text
Chapter 18 – Index Numbers
33. Compute a simple price index for each of the three items. Use 2000 as the
base period.
To compute the simple price index, take the price for a selected period and divide by the
price in the base year (Lind, 2005).
Price Quantity
Part 2000 2004 2000 2004
RC-33 $0.50 $0.60 320 340
SM-14 $1.20 $0.90 110 130
WC-50 $0.85 $1.00 230 250
P = p1 / p0 x 100
RC-33 = P = p2004 x p2000 x 100
RC-33 = P = .60 / .50 x 100
RC-33 = P = 1.2 x 100
RC-33 = 120.00
SM-14 = P = p2004 x p2000 x 100
SM-14 = P = .90 / 1.20 x 100
SM-14 = P = 0.75 x 100
SM-14 = 75.00
WC-50 = P = p2004 x p2000 x 100
WC-50 = P = 1.00 / .85 x 100
WC-50 = P = 1.1764705 x 100
WC-50 = 117.64705 or 117.6471
Lind, Marchal, & Wathen Text
Chapter 18 – Index Numbers
34. Compute a simple aggregate price index for 2004. Use 2000 as the base period.
To compute the simple aggregate price index, take the sum of the prices for a selected
period and divide by the sum of the price index in the base year (Lind, 2005).
P = (.60 + .90 + 1.00) / (.50 + 1.20 + .85) x 100
P = (2.50 / 2.55) x 100
P = 0.9803921 x 100
P = 98.03921
Lind, Marchal, & Wathen Text
Chapter 18 – Index Numbers
56. The Super Bowl is usually the TV program with the largest viewing audience each
year; therefore, many companies use the Super Bowl to launch major advertising campaigns. The cost for a 30-second spot, as reported below, has increased dramatically since the first game in 1967. Also shown is the face value of a ticket to the game for the selected years.
Year TV Commercial Game Ticket
1967 $ 42,000 $ 8.00
1988 $ 525,000 $100.00
1999 $1,600,000 $325.00
2001 $2,100,000 $325.00
2002 $1,000,000 $400.00
Go to the Bureau of Labor Statistics website www.bls.gov/data.htm, click on Most Requested Series, and find the Consumer Price Index—All Urban Consumers. Select the base as 1967, and find the CPI for the above years. Compare the rate of change in the Consumer Price Index to the cost of TV commercials and the cost of a game ticket. Write a brief report summarizing your findings.
Using the formula for change in Consumer Price Index
CPI Increase by Percentage
1967-1988 = 246.7%
1988-1999= 50.0%
1999-2001=6.5%
2001-2002=1.2%
Lind, Marchal, & Wathen Text
Chapter 18 – Index Numbers
56. (Continued).
TV Commercials
1967-1988 =1,150.0%
1988-1999= 204.8%
1999-2001=31.3%
2001-2002= (9.5%)
Game Ticket
1967-1988 =1,150.0%
1988-1999= 225.0%
1999-2001=0.0%
2001-2002= 23.2%
The most dramatic change in cost for both TV Commercials and Game Tickets came
between the years 1967-1988. Moreover, the percentage change in1988-1999 is
significant, especially since it occurred over an 11 year span. Between the years
1999-2002, prices per ticket and commercial time have been relatively unaffected. TV
commercials declined in price, and game tickets had a moderate change. This falls in line
with the CPI increase since 1967.
References
Barnes, Ryan. "Economic Indicators: Purchasing Managers Index (PMI)." Welcome to
Investopedia.com - Your Source for Investing Education. Retrieved: August 1, 2009.
Web site: <http://investopedia.com/university/releases/napm.asp>.
Cooper, D. R., & Schlinder, P.S., (2003). Business Research Methods. (8th ed.).
Chapter 7: Sampling Design. New York: McGraw-Hill.
Econometric Center. Kennesaw State University, 2006. Retrieved: August 1, 2009. Web site:
http://econometriccenter.org/Main/default.aspx?resource=About%20the%20PMI%20Ind
Emery, D. R., Finnerty, J. D. & Stowe, John D. (2007). Corporate Financial Management.
(3rd ed.). Chapter 6: Risk and Return: Stocks. Upper Saddle River, NJ: Pearson.
Lind, D. A., Marchal, W. G., & Wathen, S. A. (2005) Statistical Techniques in Business and
Economics. (12th ed.). Chapter 8: Sampling Methods and the Central Limit Theorem.
New York: McGraw-Hill.
Lind, D. A., Marchal, W. G., & Wathen, S. A. (2005) Statistical Techniques in Business and
Economics. (12th ed.). Chapter 18: Index Numbers. New York: McGraw-Hill.
References
“Notice: Data not available: U.S. Bureau of Labor Statistics." Databases, Tables & Calculators
by Subject. Retrieved: August 1, 2009. Web site:
<http://data.bls.gov/PDQ/servlet/SurveyOutputServlet>.
Sevilla, A. & Somers, K. (2007). Quantitative Reasoning: Tools for Today’s Informed Citizen.
Topic 8 – Indexes and Ratings. Emeryville, CA: Key College Publishing.
Sevilla, A. & Somers, K. (2007). Quantitative Reasoning: Tools for Today’s Informed Citizen.
Topic 18 – Basics of Probability. Emeryville, CA: Key College Publishing.
