HI6007 Statistics for Business Decisions

Tutorial 1 – Week 2

Question 1:

In your own words, differentiate the following statistical terminologies with some examples.

a. Population Parameter and Sample Statistic

b. Descriptive Statistics and Inferential Statistics

c. Nominal Scale and Ordinal Scale

d. Primary Data Source and Secondary Data Source

Question 2:

The Bureau of Transportation Statistics Omnibus Household Survey is conducted annually and serves as an information source for the U.S. Department of Transportation. In one part of the survey the person being interviewed was asked to respond to the following statement: “Drivers of motor vehicles should be allowed to talk on a hand-held cell phone while driving.” Possible responses were strongly agree, somewhat agree, somewhat disagree, and strongly disagree. Forty-four respondents said that they strongly agree with this statement, 130 said that they somewhat agree, 165 said they somewhat disagree, and 741 said they strongly disagree with this statement (Bureau of Transportation website, August 2010).

a. Do the responses for this statement provide categorical or quantitative data?

b. Would it make more sense to use averages or percentages as a summary of the responses for this statement?

c. What percentage of respondents strongly agrees with allowing drivers of motor vehicles to talk on a hand-held cell phone while driving?

d. Do the results indicate general support for or against allowing drivers of motor vehicles to talk on a hand-held cell phone while driving?

Question 3

The table below shows a data set containing information for 25 of the shadow stocks tracked by the American Association of Individual Investors. Shadow stocks are common stocks of smaller companies that are not closely followed by Wall Street analysts.

Company Exchange Ticker Symbol Market Cap ($ millions) Price/ Earnings Ratio Gross Profit Margin (%)

DeWolfe Companies AMEX DWL 36.4 8.4 36.7

North Coast Energy OTC NCEB 52.5 6.2 59.3

Hansen Natural Corp. OTC HANS 41.1 14.6 44.8

MarineMax, Inc. NYSE HZO 111.5 7.2 23.8

Nanometrics Incorporated OTC NANO 228.6 38.0 53.3

TeamStaff, Inc. OTC TSTF 92.1 33.5 4.1

Environmental Tectonics AMEX ETC 51.1 35.8 35.9

Measurement Specialties AMEX MSS 101.8 26.8 37.6

SEMCO Energy, Inc. NYSE SEN 193.4 18.7 23.6

Party City Corporation OTC PCTY 97.2 15.9 36.4

Embrex, Inc. OTC EMBX 136.5 18.9 59.5

Tech/Ops Sevcon, Inc. AMEX TO 23.2 20.7 35.7

ARCADIS NV OTC ARCAF 173.4 8.8 9.6

Qiao Xing Universal Tele. OTC XING 64.3 22.1 30.8

Energy West Incorporated OTC EWST 29.1 9.7 16.3

Barnwell Industries, Inc. AMEX BRN 27.3 7.4 73.4

Innodata Corporation OTC INOD 66.1 11.0 29.6

Medical Action Industries OTC MDCI 137.1 26.9 30.6

Instrumentarium Corp. OTC INMRY 240.9 3.6 52.1

Petroleum Development OTC PETD 95.9 6.1 19.4

Drexler Technology Corp. OTC DRXR 233.6 45.6 53.6

Gerber Childrenswear Inc. NYSE GCW 126.9 7.9 25.8

Gaiam, Inc. OTC GAIA 295.5 68.2 60.7

Artesian Resources Corp. OTC ARTNA 62.8 20.5 45.5

York Water Company OTC YORW 92.2 22.9 74.2

a. How many variables are in the data set?

b. Which of the variables are categorical and which are quantitative?

c. For the Exchange variable, show the frequency and the percent frequency for AMEx. Construct a bar graph for the Exchange variable.

d. Show the frequency distribution for the gross Profit Margin using the five intervals: 0–14.9, 15–29.9, 30–44.9, 45–59.9, and 60–74.9. Construct a histogram.

Tutorial 2 – Week 3

Question 1:

Data showing the population by state in millions of people follow (The World Almanac, 2012). The dataset in Excel file 2012Population.xlsx.

a. Develop a frequency distribution, a percent frequency distribution, and a histogram. Use a class width of 2.5 million. b. Does there appear to be any skewness in the distribution? Explain. c. What observations can you make about the population of the 50 states?

Question 2:

Dividend yield is the annual dividend paid by a company expressed as a percentage of the price of the stock (dividend/Stock price 3 100). The dividend yield for the Dow Jones Industrial Average companies is shown in the following table (The Wall Street Journal, June 8, 2009). The dataset in Excel file Dyield.xlsx

a. Construct a frequency distribution and percent frequency distribution. b. Construct a histogram. c. Comment on the shape of the distribution. d. What do the tabular and graphical summaries indicate about the dividend yields among the Dow Jones Industrial Average companies?

Question 3

Construct a cross-tabulation with Year founded as the row variable and % Graduates the column variable. Use classes starting with 1600 and ending with 2000 in increments of 50 for Year founded. For % Graduate, use classes starting with 35% and ending with 100% in increments of 5%. The dataset in Excel file Colleges.xlsx

a. Compute the row percentages for your cross-tabulation in part (a). b. Comment on any relationship between the variables

Tutorial 3 – Week 4

Question 1:

A survey of adults aged 18 and older conducted by Princess Cruises asked how many days into your vacation does it take until you feel truly relaxed (USA today, August 24, 2011). The responses were as follows: 422—a day or less; 181—2 days; 80—3 days; 121—4 or more days; and 201—never feel relaxed.

a. How many adults participated in the Princess Cruises survey?

b. What response has the highest probability? What is the probability of this response?

c. What is the probability a respondent never feels truly relaxed on a vacation? d. What is the probability it takes a respondent 2 or more days to feel truly relaxed?

Question 2:

Forty-three percent of Americans use social media and other websites to voice their opinions about television programs (the Huffington Post, November 23, 2011). Below are the results of a survey of 1364 individuals who were asked if they use social media and other websites to voice their opinions about Television programs

Uses Social Media and Other Websites to Voice Opinions About Television Programs Doesn’t Use Social Media and Other Websites to Voice Opinions About Television Programs

Female 395 291

Male 323 355

a. Show a joint probability table.

b. What is the probability a respondent is female?

c. What is the conditional probability a respondent uses social media and other websites to voice opinions about television programs given the respondent is female?

d. Let F denote the event that the respondent is female, and A denote the event that the respondent uses social media and other websites to voice opinions about television programs. Are events F and A independent?

Question 3

The following table shows the percentage of individuals in each age group who use an online tax program to prepare their federal income tax return (CompleteTax website, November 9, 2012).

Age Online Tax Program (%)

18-34 16

35-44 12

45-54 10

55-64 8

65+ 2

Suppose a follow-up study consisting of personal interviews is to be conducted to deter- mine the most important factors in selecting a method for filing taxes.

a. How many 18–34-year-olds must be sampled to find an expected number of at least 25 who use an online tax program to prepare their federal income tax return?

b. How many 35–44-year-olds must be sampled to find an expected number of at least 25 who use an online tax program to prepare their federal income tax return?

c. How many 651-year-olds must be sampled to find an expected number of at least 25 who use an online tax program to prepare their federal income tax return?

d. If the number of 18–34-year-olds sampled is equal to the value identified in part (a), what is the standard deviation of the percentage who use an online tax program?

Tutorial 1 – Week 2

Question 1:

In your own words, differentiate the following statistical terminologies with some examples.

a. Population Parameter and Sample Statistic

b. Descriptive Statistics and Inferential Statistics

c. Nominal Scale and Ordinal Scale

d. Primary Data Source and Secondary Data Source

Question 2:

The Bureau of Transportation Statistics Omnibus Household Survey is conducted annually and serves as an information source for the U.S. Department of Transportation. In one part of the survey the person being interviewed was asked to respond to the following statement: “Drivers of motor vehicles should be allowed to talk on a hand-held cell phone while driving.” Possible responses were strongly agree, somewhat agree, somewhat disagree, and strongly disagree. Forty-four respondents said that they strongly agree with this statement, 130 said that they somewhat agree, 165 said they somewhat disagree, and 741 said they strongly disagree with this statement (Bureau of Transportation website, August 2010).

a. Do the responses for this statement provide categorical or quantitative data?

b. Would it make more sense to use averages or percentages as a summary of the responses for this statement?

c. What percentage of respondents strongly agrees with allowing drivers of motor vehicles to talk on a hand-held cell phone while driving?

d. Do the results indicate general support for or against allowing drivers of motor vehicles to talk on a hand-held cell phone while driving?

Question 3

The table below shows a data set containing information for 25 of the shadow stocks tracked by the American Association of Individual Investors. Shadow stocks are common stocks of smaller companies that are not closely followed by Wall Street analysts.

Company Exchange Ticker Symbol Market Cap ($ millions) Price/ Earnings Ratio Gross Profit Margin (%)

DeWolfe Companies AMEX DWL 36.4 8.4 36.7

North Coast Energy OTC NCEB 52.5 6.2 59.3

Hansen Natural Corp. OTC HANS 41.1 14.6 44.8

MarineMax, Inc. NYSE HZO 111.5 7.2 23.8

Nanometrics Incorporated OTC NANO 228.6 38.0 53.3

TeamStaff, Inc. OTC TSTF 92.1 33.5 4.1

Environmental Tectonics AMEX ETC 51.1 35.8 35.9

Measurement Specialties AMEX MSS 101.8 26.8 37.6

SEMCO Energy, Inc. NYSE SEN 193.4 18.7 23.6

Party City Corporation OTC PCTY 97.2 15.9 36.4

Embrex, Inc. OTC EMBX 136.5 18.9 59.5

Tech/Ops Sevcon, Inc. AMEX TO 23.2 20.7 35.7

ARCADIS NV OTC ARCAF 173.4 8.8 9.6

Qiao Xing Universal Tele. OTC XING 64.3 22.1 30.8

Energy West Incorporated OTC EWST 29.1 9.7 16.3

Barnwell Industries, Inc. AMEX BRN 27.3 7.4 73.4

Innodata Corporation OTC INOD 66.1 11.0 29.6

Medical Action Industries OTC MDCI 137.1 26.9 30.6

Instrumentarium Corp. OTC INMRY 240.9 3.6 52.1

Petroleum Development OTC PETD 95.9 6.1 19.4

Drexler Technology Corp. OTC DRXR 233.6 45.6 53.6

Gerber Childrenswear Inc. NYSE GCW 126.9 7.9 25.8

Gaiam, Inc. OTC GAIA 295.5 68.2 60.7

Artesian Resources Corp. OTC ARTNA 62.8 20.5 45.5

York Water Company OTC YORW 92.2 22.9 74.2

a. How many variables are in the data set?

b. Which of the variables are categorical and which are quantitative?

c. For the Exchange variable, show the frequency and the percent frequency for AMEx. Construct a bar graph for the Exchange variable.

d. Show the frequency distribution for the gross Profit Margin using the five intervals: 0–14.9, 15–29.9, 30–44.9, 45–59.9, and 60–74.9. Construct a histogram.

Tutorial 2 – Week 3

Question 1:

Data showing the population by state in millions of people follow (The World Almanac, 2012). The dataset in Excel file 2012Population.xlsx.

a. Develop a frequency distribution, a percent frequency distribution, and a histogram. Use a class width of 2.5 million. b. Does there appear to be any skewness in the distribution? Explain. c. What observations can you make about the population of the 50 states?

Question 2:

Dividend yield is the annual dividend paid by a company expressed as a percentage of the price of the stock (dividend/Stock price 3 100). The dividend yield for the Dow Jones Industrial Average companies is shown in the following table (The Wall Street Journal, June 8, 2009). The dataset in Excel file Dyield.xlsx

a. Construct a frequency distribution and percent frequency distribution. b. Construct a histogram. c. Comment on the shape of the distribution. d. What do the tabular and graphical summaries indicate about the dividend yields among the Dow Jones Industrial Average companies?

Question 3

Construct a cross-tabulation with Year founded as the row variable and % Graduates the column variable. Use classes starting with 1600 and ending with 2000 in increments of 50 for Year founded. For % Graduate, use classes starting with 35% and ending with 100% in increments of 5%. The dataset in Excel file Colleges.xlsx

a. Compute the row percentages for your cross-tabulation in part (a). b. Comment on any relationship between the variables

Tutorial 3 – Week 4

Question 1:

A survey of adults aged 18 and older conducted by Princess Cruises asked how many days into your vacation does it take until you feel truly relaxed (USA today, August 24, 2011). The responses were as follows: 422—a day or less; 181—2 days; 80—3 days; 121—4 or more days; and 201—never feel relaxed.

a. How many adults participated in the Princess Cruises survey?

b. What response has the highest probability? What is the probability of this response?

c. What is the probability a respondent never feels truly relaxed on a vacation? d. What is the probability it takes a respondent 2 or more days to feel truly relaxed?

Question 2:

Forty-three percent of Americans use social media and other websites to voice their opinions about television programs (the Huffington Post, November 23, 2011). Below are the results of a survey of 1364 individuals who were asked if they use social media and other websites to voice their opinions about Television programs

Uses Social Media and Other Websites to Voice Opinions About Television Programs Doesn’t Use Social Media and Other Websites to Voice Opinions About Television Programs

Female 395 291

Male 323 355

a. Show a joint probability table.

b. What is the probability a respondent is female?

c. What is the conditional probability a respondent uses social media and other websites to voice opinions about television programs given the respondent is female?

d. Let F denote the event that the respondent is female, and A denote the event that the respondent uses social media and other websites to voice opinions about television programs. Are events F and A independent?

Question 3

The following table shows the percentage of individuals in each age group who use an online tax program to prepare their federal income tax return (CompleteTax website, November 9, 2012).

Age Online Tax Program (%)

18-34 16

35-44 12

45-54 10

55-64 8

65+ 2

Suppose a follow-up study consisting of personal interviews is to be conducted to deter- mine the most important factors in selecting a method for filing taxes.

a. How many 18–34-year-olds must be sampled to find an expected number of at least 25 who use an online tax program to prepare their federal income tax return?

b. How many 35–44-year-olds must be sampled to find an expected number of at least 25 who use an online tax program to prepare their federal income tax return?

c. How many 651-year-olds must be sampled to find an expected number of at least 25 who use an online tax program to prepare their federal income tax return?

d. If the number of 18–34-year-olds sampled is equal to the value identified in part (a), what is the standard deviation of the percentage who use an online tax program?

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