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Business Statistics Communicating With Numbers 2nd Edition Sanjiv Jaggia, Alison Kelly - Solutions
The total revenue for The Walt Disney Company was $35,510,000 for 2007, $37,843,000 for 2008, and $36,149,000 for 2009.a. Deflate the total revenue with the relevant price index.b. Discuss the revenue trend during the 2007-2009 period using nominal as well as real values?
According to the New Hampshire Department of Education, the average teacher salary in public school districts in New Hampshire was $46,797 in 2006, $48,310 in 2007, and $46,797 in 2008. Comment on the percentage change in the dollar value (nominal) as well as the purchasing power (real) of salaries?
According to Fisher College of Business at the Ohio State University, the starting salary of their graduates in the MBA program in 2008 was $89,156. What must be the starting salary of the MBAs in 2009 if the salary increase makes the exact cost of living adjustment?
Kim Baek invested $20,000 for a year in corporate bonds. Each bond sold for $1,000 and earned a coupon payment of $80 each during the year. The price of the bond at the end of the year has dropped to $980.a. Calculate Kim's investment return.b. Calculate Kim's total dollar gain or loss on his
Toyota Motor Corp., once considered a company synonymous with reliability and customer satisfaction, has been engulfed in a perfect storm with millions of cars recalled (BBC News, March 19, 2010). The following table shows the monthly adjusted closing price per share of Toyota from October 2009 to
Consider the following price data from 2002 to 2010.a. Compute the simple price index using 2002 as the base year.b. Update the index numbers with a base year revised from 2002 to 2005.c. Plot the index numbers with a base year of 2002 and a base year of 2005. Compare the two plots?
Consider the following price data from 2009 to 2011a. Compute and interpret the simple price index for each product, using 2009 as the base year.b. Compute and interpret the un-weighted aggregate price index, using 2009 as the base year?
Let the quantities corresponding to the prices in Exercise 36 be given by the following table.a. Compute the Laspeyres price index, using 2009 as the base year.b. Compute the Paasche price index, using 2009 as the base year.c. Comment on the differences between the two indices?
Lindsay Kelly bought 100 shares of Google, 300 shares of Microsoft, and 500 shares of Nokia in January 2005. The adjusted closing prices of these stocks over the next three years are shown in the accompanying table.a. Compute and interpret the unweighted aggregate price index for Lindsay's
Citigroup, Inc., is a major financial services company based in New York. It suffered huge losses during the global financial crisis and was rescued in November 2008 in a massive bailout by the U.S. government. Consider the following table, representing the net revenue and net income of Citigroup
The year-end price and dividend information on a stock is given in the following table.Year................. Price........... Dividend1 ...................$23.50.................. na2..................... 24.80.............. $0.183..................... 22.90............... 0.12a. What is the
Consider the following consumer price index and producer price index for 2006-2009.a. Use the relevant price index to deflate the data on net revenue of Citigroup, given in Exercise 39.b. Use the relevant price index to deflate the data on net income of Citigroup, given in Exercise 39?
An investor bought 1,000 shares of Citigroup in January 2009 for $3.55 a share. She sold all of her shares in December 2009 for $3.31 a share.a. What annual rate of return did the investor earn?b. Use the CPI information from Exercise 40 to compute the inflation rate for 2009.c. What is the
The adjusted closing prices of Wendy's/Arby's Group, Inc., for the first three months of 2008 are presented in the following table. Also included in the table is the corresponding consumer price index (CPI).Date.................. Adjusted Closing Price.................. CPI (Base 1982-1984)January,
A portfolio manager invested $1,500,000 in bonds in 2007. In one year the market value of the bonds dropped to $1,485,000. The interest payments during the year totaled $105,000. a. What was the manager's total rate of return for the year? b. What was the manager's real rate of return if the
Bill Anderson purchased 1,000 shares of Microsoft Corporation stock for $17,100 at the beginning of 2009. At the end of the year, he sold all of his Microsoft shares at $30.48 a share. He also earned a dividend of $0.52 per share during the year. a. What is Bill's total return on the investment? b.
You would like to invest $20,000 for a year in a riskfree investment. A conventional certificate of deposit (CD) offers a 4.6% annual rate of return. You are also considering an "Inflation-Plus" CD which offers a real rate of return of 2.2% regardless of the inflation rate.a. What is the implied
Consider the following adjusted closing stock prices for Intel Corporation. Find the monthly returns for November and December of 2010. Date................................. Adjusted Closing Price December 2010....................................... $21.48 november
Consider the following adjusted closing stock prices for Johnson and Johnson (J&J) and Caterpillar, Inc. Compute and compare the monthly returns for both companies. Date....................... J&J................... Caterpillar March 2011............ 60.70........................ 99.86 February
The dot-com period, roughly between 1995-2000, was characterized by extreme investor optimism for Internet-based businesses. This period was also marked by young, bold managers, who made a good deal of money by reaching consumers only over the Internet. Arguably, the dot-com boom was a case of too
The U.S. is often blamed for triggering the 2008 global financial crisis because many of the excesses and bad practices originated in the U.S. The crisis has had consequences on all aspects of the global economy. According to a recent report by Brookings Institute, the U.S. economic crisis is
The Cheesecake Factory, Inc., is a popular restaurant chain in the U.S. Although it started as a small restaurant in 1978, it currently has over 140 branches all over the country. The restaurants are characterized by extensive menus, custom décor, and large portions of food. Jeff Watson works as
Consider the following competing hypotheses and sample data.H0: m = 20HA: m ≠ 20n = 7T- = 2T+ = 26a. Specify the decision rule at the 5% significance level.b. What is the conclusion? Explain.
A realtor in Mission Viejo, California, believes that the median price of a house is more than $500,000.a. Specify the competing hypotheses for the test.b. Using the MV_Houses data, calculate the value of the test statistic. Assume the normal approximation for T.c. Calculate the p-value.d. At the
An entrepreneur examines monthly sales (in $1,000s) for 40 convenience stores in Rhode Island.a. Specify the competing hypotheses to determine whether median sales differ from $130,000.b. At the 5% significance level, what is the decision rule? Assume the normal approximation for T.c. Using the
Consider the following competing hypotheses and accompanying sample data drawn from a matched-pairs sample.H0: mD ≥ 0HA: mD < 0n = 9T- = 40 T+ = 5a. Specify the decision rule at the 5% significance level.b. What is the conclusion?
Consider the following competing hypotheses and accompanying sample data drawn from a matched-pairs sample.H0: mD = 0HA: mD ≠ 0n = 50T- = 400 T+ = 875a. Determine the value of the test statistic using a normal approximation for T.b. Calculate the p-value.c. At the 5% significance level, what is
The following table contains information on a matched-pairs sample.a. Specify the competing hypotheses that determine whether the median difference between Population 1 and Population 2 is less than zero.b. With α = 0.05, what is the decision rule?c. Calculate the value of the test statistic
The following data are derived from a matched-pairs sample.a. Specify the competing hypotheses that determine whether the population median difference differs from zero.b. Assuming that T is normally distributed, determine the value of the test statistic.c. Calculate the p-value.d. At the 1%
Consider the following competing hypotheses and accompanying data drawn from two independent populations.H0: m1 - m2 = 0.... W1 = 80..... W2 = 40HA: m1 - m2 ≠ 0.... n1 = 7......... n2 = 8a. Specify the decision rule at the 5% significance level.b. Determine the value of the test statistic.c. What
Consider the following competing hypotheses and accompanying data drawn from two independent populations.H0: m1 - m2 ≥ 0 W1 = 20 W2 = 35HA: m1 - m2 < 0 n1 = 5 n2 = 5a. Specify the decision rule at the 5% significance level.b. Determine the value of the test statistic.c. What is the conclusion?
The following data were randomly drawn from two independent populations.a. Specify the competing hypotheses to determine whether the median of Population 1 is less than the median of Population 2.b. With α = 0.05, what is the decision rule?c. Calculate the value of the test statistic W.d. Is the
The following data were randomly drawn from two independent populations.a. Specify the competing hypotheses to determine whether the median of Population 1 is greater than the median of Population 2.b. With α = 0.05, what is the decision rule?c. Calculate the value of the test statistic W.d. Is
Consider the following competing hypotheses and sample data.H0: m ≥ 150HA: m < 150n = 9 T- = 42 T+ = 3a. Specify the decision rule at the 1% significance level.b. What is the conclusion? Explain.
The following data are provided for two samples drawn from independent populations: W = 700, n1 = 25, and n2 = 20. Suppose the distribution of W is approximately normal.a. Calculate the mean and the standard deviation of the distribution of W.b. Specify the competing hypotheses to determine whether
The following data are provided for two samples drawn from independent populations: W = 545, n1 = 25, and n2 = 25. Suppose the distribution of W is approximately normal.a. Calculate the mean and the standard deviation of the distribution of W.b. Specify the competing hypotheses to determine whether
Suppose eight college-bound students take a mock SAT, complete a three-month testprep course, and then take the real SAT. A portion of the data is shown in the accompanying table.Student..................... Score on Mock SAT............... Score on Real
A diet center claims that it has the most effective weight loss program in the region. Its advertisement says "Participants in our program really lose weight." Five clients of this program are weighed on the first day of the diet and then three months later.Client................... Weight on First
A bank employs two appraisers. When approving borrowers for mortgages, it is imperative that the appraisers value the same types of properties consistently. To make sure that this is the case, the bank asks the appraisers to value 10 different properties. A portion of the data sis shown in the
A professor teaches two sections of an introductory statistics course. He gives each section the same final and wonders if any significant differences exist between the medians of these sections. He randomly draws a sample of seven scores from Section A and six scores from Section B.a. Set up the
A recent analysis of census data suggests that married men have a higher median income than unmarried men (The Boston Globe, January 19, 2010). Suppose the incomes (in $1,000s) of six married men and seven unmarried men produce the following representative results:a. Set up the hypotheses to test
According to the Organization of Economic Cooperation and Development, South Koreans spend more hours per year on the job than people in any other developed country (The Wall Street Journal, March 1, 2010). Suppose 10 workers in South Korea and 10 workers in the United States are asked to report
Researchers at the Wharton School of Business have found that men and women shop for different reasons. While women enjoy the shopping experience, men are on a mission to get the job done. Men do not shop as frequently, but when they do, they make big purchases like expensive electronics. The
Consider the following sample information: k = 3 and H = 4.5.a. Specify the competing hypotheses to test whether some differences exist between the medians.b. At the 10% significance level, specify the critical value and the decision rule.c. Do some medians differ? Explain.
Consider the following competing hypotheses and sample data.H0: m ≤ 150HA: m > 150n = 30 T - = 200 T+ = 265a. Assuming that the sampling distribution of T is normally distributed, determine the value of the test statistic.b. Calculate the p-value.c. At the 5% significance level, what is the
Consider the following sample information: k = 5 and H = 12.4.a. Specify the competing hypotheses to test whether some differences exist between the medians.b. Approximate the p-value.c. At the 5% significance level, do some medians differ? Explain.
Random samples were drawn from three independent populations. The results are shown in the accompanying table.a. Specify the competing hypotheses to test whether some differences exist between the medians.b. Calculate the value of the test statistic H.c. At the 10% significance level, what is the
Random samples were drawn from four independent populations. The results are shown in the accompanying table.a. Specify the competing hypotheses to test whether some differences exist between the medians.b. Calculate the value of the test statistic H.c. Approximate the p-value.d. At the 1%
A research analyst wants to test whether the median unemployment rate differs from one region of the country to another. She collects the unemployment rate (in percent) of similar-sized cities in three regions of the United States. The results are shown in the accompanying table.a. Specify the
A quality-control manager wants to test whether there is any difference in the median length of life of light bulbs between three different brands. Random samples were drawn from each brand where the duration of each light bulb (in hours) was measured. The results are shown in the accompanying
A research analyst examines annual returns (in percent) for Industry A, Industry B, and Industry C, as shown in the accompanying table.Industry A.................... Industry B........................... Industry C16.86..................................
A well-known conglomerate claims that its detergent "whitens and brightens better than all the rest." In order to compare the cleansing action of the top three detergents, 15 swatches of white cloth were soiled with red wine and grass stains and then washed in front-loading machines with the
Consider the following competing hypotheses and accompanying sample data.H0: ρS = 0HA: ρS ≠ 0rS = 0.92 and n = 8a. Specify the decision rule at the 1% significance level.b. What is the value of the test statistic?c. What is the conclusion?
Consider the following sample data.8 5 11 7 6 5a. Specify the competing hypotheses to determine whether the median is less than 10.b. With α = 0.05, what is the decision rule?c. Calculate the value of the test statistic T.d. Is the median less than 10? Explain
Consider the following competing hypotheses and accompanying sample data.H0: ρS ≥ 0HA: ρS < 0rS = 0.64 and n = 9a. Specify the decision rule at the 5% significance level.b. What is the value of the test statistic?c. What is the conclusion?
Consider the following sample data:a. Calculate and interpret rs.b. Specify the competing hypotheses to determine whether the Spearman rank correlation coefficient differs from zero.c. At the 5% significance level, what is the decision rule?d. What is the conclusion?
Consider the following sample data:a. Calculate and interpret rs.b. Specify the competing hypotheses to determine whether the Spearman rank correlation coefficient is less than zero.c. At the 1% significance level, what is the decision rule?d. What is the conclusion?
Consider the following competing hypotheses and accompanying sample data.H0: ρS = 0HA: ρS ≠ 0rS = 0.85 and n = 65a. What is the value of the test statistic and its associated p-value? Assume the normal approximation for rS.b. At the 10% significance level, what is the conclusion?
Consider the following competing hypotheses and accompanying sample data.H0: ρS ≤ 0HA: ρS > 0rS = 0.64 and n = 50a. What is the value of the test statistic and its associated p-value? Assume the normal approximation for rS.b. At the 1% significance level, what is the conclusion?
The following table shows the ranks given by two judges to the performance of six finalists in a men's figure skating competition:a. Calculate and interpret the Spearman rank correlation coefficient rs .b. Specify the competing hypotheses to determine whether the Spearman rank correlation
The following table shows the World Bank's 2008 ranking of the richest countries, as measured by per capita GNP. In addition, it gives each country's respective rank with respect to infant mortality according to the Central Intelligence Agency. A higher rank indicates a lower mortality rate.a.
You are interested in whether the returns on Asset A are negatively correlated with the returns on Asset B. Consider the following annual return data on the two assets:........................Asset A....................... Asset BYear 1...................-20%......................................
In an attempt to determine whether a relationship exists between the price of a home and the number of days it takes to sell the home, a real estate agent collected the following data from recent sales in his city.Price (in $1,000s)..................... Days to Sell
The director of graduate admissions at a local university is analyzing the relationship between scores on the Graduate Record Examination (GRE) and subsequent performance in graduate school, as measured by a student's grade point average (GPA). She uses a sample of 7 students who graduated within
Consider the following sample data.105 90 110 80 85 85 103 70 115 75Assume the normal approximation for T.a. Specify the competing hypotheses to determine whether the median differs from 100.b. Determine the critical value(s) of the test at α = 0.10.c. Calculate the value of the test statistic.d.
A social scientist analyzes the relationship between educational attainment and salary. For 65 individuals he collects data on each individual's educational attainment (in years) and his/her salary (in $1,000s). He then calculates a Spearman rank correlation coefficient of 0.85.a. Specify the
An engineer examines the relationship between the weight of a car and its average miles per gallon (MPG). For a sample of 100 cars, he calculates a Spearman rank correlation coefficient of -0.60.a. Specify the competing hypotheses to determine whether the Spearman rank correlation coefficient is
Many attempts have been made to relate happiness with various factors. One such study relates happiness with age and finds that, holding everything else constant, people are least happy when they are in their mid-40s (The Economist, December 16, 2010). The accompanying table shows a portion of data
The accompanying table shows a portion of the number of cases of crime related to gambling and offenses against the family and children for the 50 states in the United States during 2010.Using the Spearman rank correlation coefficient, determine whether gambling and family abuse are correlated at
Consider the following competing hypotheses and sample data.H0: p = 0.50HA: p ≠ 0.50n = 40 = 0.30a. Calculate the value of the test statistic for the sign test.b. Calculate the p-value.c. At the 5% significance level, what is the conclusion? Explain.
Consider the following competing hypotheses and sample data.H0: p ≤ 0.50HA: p > 0.50n = 25 = 0.64a. At the 1% significance level, what is the decision rule?b. Calculate the value of the test statistic for the sign test.c. What is the conclusion? Explain.
Consider the following sign data, produced from a matched-pairs sample of ordinal data.+ + + - + + - + + + + - + + - - + + + +a. Specify the competing hypotheses to determine whether the proportion of negative signs differs from the proportion of positive signs.b. Calculate the value of the test
Consider the following sign data, produced from a matched-pairs sample of ordinal data.+ - - + - - + - + - + - - - + -a. Specify the competing hypotheses to determine whether the proportion of negative signs is significantly greater than the proportion of positive signs.b. At the 1% significance
Concerned with the increase of plastic water bottles in landfills, a leading environmentalist wants to determine whether there is any difference in taste between the local tap water and the leading bottled water. She randomly selects 14 consumers and conducts a blind taste test. She asks the
In March 2009, 100 registered voters were asked to rate the "effectiveness" of President Obama. In March 2010, these same people were again asked to make the same assessment. Seventy percent of the second ratings were lower than the first ratings and 30% were higher.a. Using the sign test, specify
A random sample of eight drugstores shows the following prices (in $) for a popular pain reliever:5.00 4.25 3.75 5.50 5.75 6.25 5.25 4.25a. Specify the competing hypotheses to determine whether the median price is less than $4.50.b. At the 5% significance level, what is the decision rule?c.
For scholarship purposes, two graduate faculty members rate 12 applicants to the PhD program on a scale of 1 to 10 (with 10 indicating an excellent candidate). These ratings are shown in the following table.a. Using the sign test, specify the competing hypotheses to determine whether the ratings
A new diet and exercise program claims that it significantly lowers a participant's cholesterol level. In order to test this claim, a sample of 60 participants is taken. Their cholesterol levels are measured before and after the three-month program. Forty of the participants recorded lower
Consider the following information: n1 = 24, n2 = 28 and R = 18, where R is the number of runs, n1 and n2 are the number of elements in a sequence possessing and not possessing a certain attribute, and n1 + n2 = n.a. Specify the competing hypotheses to test for nonrandomness.b. Calculate the value
Consider the following information: n1 = 10, n2 = 13 and R = 8, where R is the number of runs, n1 and n2 are the number of elements in a sequence possessing and not possessing a certain attribute, and n1 + n2 = n.a. Specify the competing hypotheses to test for nonrandomness.b. Calculate the value
Let A and B be two possible outcomes of a single experiment. The sequence of the outcomes is as follows:BBAABAABBABABBBABBAAABABBABBABAAt the 5% significance level, conduct a hypothesis test to determine if the outcomes are nonrandom.
Let D denote a desirable outcome and U denote an undesirable outcome. The sequence of the outcomes is as follows:DDDUUDUUUUUDDDUUDUUUDDDUUUUDDDAt the 1% significance level, conduct a hypothesis test to determine if the outcomes are nonrandom.
Given the digits zero through nine, a computer program is supposed to generate even and odd numbers randomly. The computer produced the following sequence of numbers:5 3 4 6 8 0 2 9 7 7 1 6 8 3 1 5 2 4 3 3 9 2a. Specify the competing hypotheses to test for nonrandomness.b. At the 1% significance
A gambler suspects that a coin may be weighted more heavily toward the outcome of tails (T) over heads (H). He flips the coin 25 times and notes the following sequence:T T H T T T H H T H T T H T T T H H T H T H TT Ha. Specify the competing hypotheses to test the gambler's belief on
The following table shows a portion of the growth rate in the gross domestic product (GDP) for India from 1980 through 2008. Use the method of runs above and below the median with a significance level of 5% to test the null hypothesis of randomness against the alternative that there is a trend or
The superintendent of a large suburban high school must decide whether to close the school for at least two days due to the spread of flu. If she can confirm a trend in absenteeism, then she will close the high school. The following are the number of students absent from the high school on 25
The following table lists the annual returns (in percent) over a 10-year period for ING Russia, a top-performing mutual fund.a. Specify the competing hypotheses to determine whether the median return differs from 8%.b. At the 10% significance level, what is the decision rule? Do not assume the
A research analyst follows the biotechnology industry and examines the daily stock price of Amgen, Inc. over the past year. The table below shows a portion of the daily stock price of Amgen for the 252 trading days in 2010. The research analyst wants to test the random-walk hypothesis that suggests
The following are the closing stock prices for a pharmaceutical firm over the past two weeks.a. Specify the competing hypotheses to determine whether the median stock price is greater than $61.25.b. At the 5% significance level, what is the decision rule? Do not assume that the sampling
A farmer is concerned that a change in fertilizer to an organic variant might change his crop yield. He subdivides 6 lots and uses the old fertilizer on one half of each lot and the new fertilizer on the other half. The following table shows the results.Lot ..............Crop Yield Using Old
The table below shows a portion of the returns for Fidelity's Equity Income mutual fund and Vanguard's Equity Income mutual fund from 2000 through 2010.Year................... Fidelity.................... Vanguard2000....................... 3.88.........................
A consumer advocate researches the length of life between two brands of refrigerators, Brand A and Brand B. He collects data on the longevity of 40 refrigerators for Brand A and repeats the sampling for Brand B. A portion of the data is shown in the accompanying table.Brand A.....................
A psychiatrist believes that the location of a test center may influence a test taker's performance. To test his claim, he collects SAT scores from four different locations.a. Specify the competing hypotheses to test whether some median test scores differ by location.b. At the 5% significance
An economist wants to determine whether the Price/Earnings (P/E) ratio is the same for firms in three industries. Five firms were randomly selected from each industry. Their P/E ratios are shown in the accompanying table.a. Specify the competing hypotheses to test whether some median P/E ratios
The following table shows a portion of the annual returns (in percent) for two of Fidelity's mutual funds: the Fidelity Advisor's Electronic Fund and the Fidelity Advisor's Utilities Fund.Year........................ Electronics..................... Utilities2001................................
A research analyst believes that a positive relationship exists between a firm's advertising expenditures and its sales. For 65 firms, she collects data on each firm's yearly advertising expenditures and subsequent sales. She calculates a Spearman rank correlation coefficient of 0.45.a. Specify the
In order to ensure the public's health and safety, state health inspectors are required to rate the cleanliness and quality of all restaurants in the state. Restaurants that consistently score below a certain level often lose their licenses to operate. From a sample of 10 restaurants, two health
During the fourth quarter of 2009, rents declined in almost all major cities in the United States. The largest fall was in New York, where average rents fell nearly 20% to $44.69 per square foot annually (The Wall Street Journal, January 8, 2010). The following table lists the average rent per
The following table shows a portion of the growth rate in the gross domestic product (GDP) for China from 1980 through 2008. Use the method of runs above and below the median with a significance level of 5% to test the null hypothesis of randomness against the alternative that there is a trend or
A research analyst follows the monthly price data for the Dow Jones Industrial Average for the years 2008-2010. The accompanying table shows a portion of the price data. The analyst wants to test the random-walk hypothesis that suggests that prices move randomly over time with no discernible
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