# ST 350 Homework 4

ST 350 HW #4 Spring 2019 (Homework)

Six months ago you won \$1,000,000 on a scratch­off lottery ticket and invested your winnings with a financial advisor at the investment firm Dewey, Lie, and Howe. The earnings on the investment are compounded monthly.

You complain to the financial advisor that your returns after 6 months are inadequate and do not even cover the advisor's fees. The 6 monthly interest rates (in decimal form) have been R1 = ­0.4, R2 = 0.67, R3 = 1.0, R4 = ­0.5, R5 = 0.2, R6 = ­0.165.

Question 1. What is the total worth of your investment after 6 months? \$1,004,004

The financial advisor responds that you shouldn't complain because the average return over the 6 months has been an impressive 13.4% (0.134 in decimal form). You angrily respond that the average return is not representative of the 6­month investment performance, and that the geometric mean should be used instead.

Question 2. What is the geometric mean of the above monthly returns? (express as a decimal; round off to 3 decimal places)

.001  geometric mean

1. 3/3 points | Previous Answers

Rather than getting a summer job or internship to increase his \$500 savings account balance, a member of the Poole College of Management student investment club decides to put his \$500 to work by making an investment. He pools his \$500 with the money contributed by the other members of the investment club and the club makes a 10­week investment in bitcoin. The investment returns are compounded on a weekly basis. The 10 weekly return rates, in decimal form, are in this Excel file Bitcoin Returns. Note that the average (mean) weekly return rate, to 4 decimal places, is r = .0814.

Question 1. At the end of 10 weeks this member of the investment club is disappointed with the results of his \$500 investment. He has used the simple interest formula I = Prt, where I = interest, P = his principal (\$500), r = average weekly return rate, and t = time (10 weeks) to calculate what he thinks the terminal value of his investment should be. What is his calculated terminal value (principal + interest)?

\$907

Question 2a. Since the returns are compounded weekly, you will show the student the correct terminal value by using the geometric mean. What is the geometric mean return rate of this investment? Express your answer as a decimal, not a percentage, rounded to 4 decimal places.

0.0152

Question 2b. What is the terminal value of this investment? \$581.40

1. 5/3.5 points | Previous Answers

You must choose an SRS of 10 of the 452 retail outlets in New York that sell your company's product.

Question 1. How would you label this population? (Start at 001, not 000).

001  to 452

Question 2. Use this random digits table, starting at line 122, to choose your sample. Which retail outlets would you select? (list the number labels of the outlets that you select in the order in which you select them from the random number table as you move from left to right; also, proceed continuously from row 122 to 123, that is, use the "1" at the end of row 122 with the first 2 digits of row 123 to form the number 154).

1. 6/6 points | Previous Answers

Accountants use stratified samples during audits to verify a company's records of such things as accounts receivable. The stratification is based on the dollar amount of the item and often includes 100% sampling of the largest items. One company reports 5000 accounts receivable. Of these, 100 are in amounts over \$50,000; 500 are in amounts between \$1000 and \$50,000; and the remaining 4400 are in amounts under \$1000. Using these groups as strata, you decide to verify all of the largest accounts and to sample 5% of the midsize accounts and 1% of the small accounts.

 001 to 500 0001 to 4400

Question 1. How would you label the two strata from which you will sample?

for the midsize accounts

for the small accounts

Question 2. Use this random digits table, starting at line 115, to select only the first 5 accounts from each strata. List them below in the order in which they occur in the table. Choose the midsize accounts first. After you choose the five midsize accounts, to choose the small accounts start in row 115 from where you finished choosing the five midsize accounts.

Midsize group:

417  494  322          247        097

Small group:

3698  1452  2605          2480        3716

1. 11/11 points | Previous Answers

You are planning a sample survey that involves selecting 11 of the 100 counties in North Carolina. Your sample will be a stratified sample consisting of the 6 most populous counties in the state and 5 counties randomly selected from the remaining 94 counties.

The Excel worksheet has an alphabetical listing of all 100 North Carolina counties in column A and population estimates for July 1, 2011 and July 1, 2012 in columns D and E, respectively.

We will use the population values for July 1, 2012 in column E. To simplify the selection of the 11 counties, we will order the counties according to their July 1, 2012 populations.

Order the counties by July 1, 2012 population as follows: Excel 2003

highlight the cell range A5:E105

in the Excel menu bar click on "Data"; in the drop­down menu click "Sort" near the bottom of the Sort dialogue box click the radio button next to "Header row" in the first "Sort by" window choose "2012" and make sure that the "Ascending" radio button is selected click OK

Excel 2007 and later

highlight the cell range A5:E105

Click the "Home" tab at the upper left of the Excel window

at the far right of the menu ribbon click on the "Sort and Filter" icon

In the drop­down menu click on "Custom Sort..."

In the upper right­hand corner of the Sort window make sure the box next to "My data has headers" has a check mark; if it does not have a check mark, click in the box to make a check mark appear.

In the Sort window, under Column, sort by "2012"

In the Sort window, under Sort On, choose "values"

In the Sort window, under Order, choose "A to Z" Click OK

The counties should now be listed in increasing order according to their July 1, 2012 populations. Tyrell County should be listed first (in row 6) with July 1, 2012 population 4,338.

Question 1. Scroll down to the bottom of the worksheet to see the most populous counties. List below the 6 most populous counties and their populations. List the most populous county first and use commas in your population answers.

1. (most populous) Mecklenburg County; population 969,031

County; population 952,151

County; population 500,879

 358,137
 Forsyth
1. County; population
2. Cumberland County; population 324,049
3. (6th most populous) Durham County; population 279,641

Question 2. You would now like to select a random sample of 5 counties from the remaining 94 counties in rows 6 through 99 of the spreadsheet. To select the counties use this random digits table and use the row numbers 06 through 99 in the Excel spreadsheet as the number assigned to each county. Enter the table of random digits at line 131 and select the random sample of 5 counties using the consecutive pairs of digits 05 00 71, and so on, as you proceed from left to right in line 131. List the counties and their populations (use commas in your population answers) in the order in which they are selected using the random number table.

1. Lincoln County; population 79,313
2. Chatham County; population 65,976
3. Anson County; population 26,351
4. Brunswick County; population 112,257
5. Mitchell County; population 15,368
6. 5/1.5 points | Previous Answers

The list of individuals from which a sample is actually selected is called the sampling frame. Ideally, the sampling frame should list every individual in the population, but in practice this is often difficult. A sampling frame that leaves out part of the population is a common source of undercoverage.

In the following questions select all choices that apply; to receive credit for the question you must select all the correct choices and only the correct choices.

 Households with unlisted numbers. Poor households (cannot afford a phone) Households with a second line for the fax machine. Households without telephones. Households with more than one line. Households that connect to the internet with their phone line. Households that have moved into the community since the most recent community telephone directory was printed. Households that possess only cellphones

Question 1. A pollster wants to select a random sample of households in a particular community. The pollster randomly selects a sample of households in the community from the community telephone directory available in the public library. What households are omitted from this sampling frame?

 people who choose not to list their numbers jobless people who have moved into the community to look for employment since the most recent community telephone directory was printed people who graduated from UNC­Chapel Hill lower income people (cannot afford a phone) people who drive hybrid automobiles high income people people who choose not to have phones

Question 2. What types of people do you think are most likely to live in the omitted households selected in question 1? These people will probably be underrepresented in the sample.

 Households with unlisted numbers Households that possess only cellphones Poor households (cannot afford a phone) Households with land­line telephones that have moved into the community since the most recent community telephone directory was printed. Households without telephones

Question 3. It is usual in telephone surveys to use random dialing equipment that selects the last four digits of a telephone number at random after being given the land­line exchange (the first three digits; note that cell phone exchanges differ from land­line exchanges). Which of the households you selected in Question 1 above will be included in this sampling frame by random digit dialing?

1. 3/3 points | Previous Answers

The last stage of the Current Population Survey chooses addresses within small areas called blocks. The method used is systematic random sampling. An example will illustrate the idea of a systematic sample. Suppose that we must choose 4 addresses out of 100. Because 100/4=25, we can think of the list as four lists of 25 addresses. Choose 1 of the first 25 at random. The sample will contain this address and the addresses 25, 50, and 75 places down from it. If 13 is chosen, for example, then the systematic random sample consists of the addresses numbered 13, 38, 63, and 88.

Question 1. Use this random digits table to choose a systematic random sample of 5 addresses out of 200. Enter the table at line 120

The addresses numbered 35  75  115  155  195  are selected (list the numbers in increasing order).

 True False

Question 2. The systematic random sample above gives all individuals the same chance to be chosen.

 True False

Question 3. A systematic random sample is a simple random sample.

1. 2/2 points

The Pack Poll is a website maintained by a group of NC State undergrads under the supervision of faculty member Dr. Michael Cobb. Pack Poll conducts frequent high­quality polling of NC State students on a variety of topics of interest to students.

During the Fall and Spring semesters The Pack Poll conducts a major poll of NC State undergraduate students on a variety of topics of current interest. The Fall 2013 poll results are shown here (click the red download arrow to open the pdf report file).

The Pack Poll website has the following description of the Fall 2013 poll:

The PackPoll is a representative survey of 1,032 NCSU undergraduates. The survey was conducted over the internet using email to sample students between Nov 7­12, 2013. The response rate was 23%, and the margin of sampling error is +/­2.97%

 All NC State undergraduates. All NC State undergraduates that live on campus.    All NC State undergraduates except Fall 2013 foreign exchange students. All NC State undergraduates that were sent an email, whether they responded or not. All NC State undergraduates that have a computer. NC State undergraduates that responded to the email.

Question 1. For the Fall 2013 Pack Poll survey identify the population of interest.

Question 2. Pack Poll conducted the survey by sending an email to email addresses randomly selected from a list of all undergraduate email addresses provided by NCSU Registration & Records. What is the sampling frame?

 The proportion of all NC State undergraduates that think textbooks costs are too high. The proportion of all NC State undergraduates that think tuition is too high.    The proportion of NC State undergraduates who drive to campus that think parking costs are too high. The proportion of all NC State undergraduates that think things are generally headed in the right direction The proportion of NC State undergraduates who live off­campus that are satisfied with the Wolfline bus service.

Question 3. For the third question "Do you think things at NC State are:" the population parameter of interest is:

 Students in randomly selected on­campus courses filled out the surveys during a class lecture. Pollsters rode Wolfline busses and collected data from randomly selected riders.    Students were instructed in the email to go to a tent at the brickyard to answer survey questions. Pollsters walked around campus with a clipboard and collected data from randomly selected students. Students answered questions at a website whose link was given in the email. Pollsters went to the dorm rooms of the undergraduate students that were sent an email by Pack Poll. Students were called on their cellphone.

Question 4.. How was the data collected?

1. 1/1 points

"Why did they take my favorite show off the air?" Why did the writers

for "Family Guy" kill off the family dog Brian Griffin?".

The answer usually has to do with low Nielsen ratings. What is the Nielsen rating system anyway?

Electronic metering technology is at the heart of the Nielsen ratings process. Nielsen Media Research gives TV monitoring meters to a sample of 4,500 "Nielsen households" carefully selected from the population of 115.6 million TV households in the United States. The TV meters capture Nielsen household information on whats being viewed and when and, in the major U.S. markets, specifically who and how many in the Nielsen households are watching.

Nielsen results for a program are usually reported in two measurements, rating points/shares. A ratings point represents one percent of all US TV households; a share is the percentage of US TV households with a television set in use that is viewing the program.

For example, if Nielsen reports the results for a particular program as 8.9/14, this means that, on average, 8.9% of all US TV households were tuned in to the show during the broadcast and 14% of the households with a television in use were viewing the program.

 All US televisions. All US adults 18 and older who are watching TV.    All Nielsen TV households. All US TV households that use cable but not satellite. All US TV households.

Question 1. What is the population of interest to Nielsen Media Research?

During the Super Bowl the Nielsen results for the advertisements are of great interest, primarily because a 30­second Super Bowl advertisement costs approximately \$4 million. During a recent Super Bowl this add (right­click the link and choose "Open in new tab" or "Open in new window"; after a few seconds you can skip the annoying ad) for Doritos was one of the most popular.

Question 2. If the Nielsen results for the Doritos ad were 46.4/59, what is the estimate of the number of US TV households that viewed the Doritos ad? Your answer should be in units of millions of households; round your answer to 2 decimal places. 53.64  million US TV households.

10.2/2 points

The escalating cost of higher education has received a great deal of attention in the media as more students and their families struggle to pay for college.

Due to the high level of interest, you choose this topic for a semester project assignment in an Economics class. To obtain the data for your project you contact YouGov with a series of 11 carefully worded questions. You request that YouGov obtain responses to your questions from 1,000 US adults selected from their worldwide opt­in online panel of 2.5 million participants.

A short time later YouGov sends you This Report. Use the information in the report to answer the following questions about the responses.

 39% 49%    25% 12% 35% 22%

Question 1. What percentage of respondents in the South are of the opinion that college today is so expensive, it costs more than it's worth?

Question 2. Which one of the following groups is most likely to strongly favor making tuition free for college students?

 females Hispanic    18­29 age group residents of the Northeast Democrats those with family incomes between 40 and 80 thousand dollars

Question 3. Which one of the following charts is a correct representation of data from the YouGov report?

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