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Essentials Of Business Statistics Communicating With Numbers 1st Edition Sanjiv Jaggia, Alison Kelly - Solutions
A data set has a mean of 500 and a standard deviation of 25.a. Using Chebyshev’s theorem, find the interval that encompasses at least 75% of the data.b. Using Chebyshev’s theorem, find the interval that encompasses at least 89% of the data.
Data are drawn from a bell-shaped distribution with a mean of 20 and a standard deviation of 2.a. What percentage of the observations fall between 18 and 22?b. What percentage of the observations fall between 16 and 24?c. What percentage of the observations are less than 16?
Data are drawn from a bell-shaped distribution with a mean of 5 and a standard deviation of 2.5.a. What percentage of the observations are positive?b. What percentage of the observations are not positive?
Consider a sample with 10 observations of 23, 8, 4, 2, 24, 15, 6, 0, 24, and 5. Use z-scores to determine if there are any outliers in the data; assume a bell-shaped distribution.
A sample of the salaries of assistant professors on the business faculty at a local university revealed a mean income of $72,000 with a standard deviation of $3,000.a. Using Chebyshev’s theorem, what percentage of the faculty earns at least $66,000 but no more than $78,000?b. Using Chebyshev’s
The historical returns on a portfolio had an average return of 8 percent and a standard deviation of 12 percent. Assume that returns on this portfolio follow a bell-shaped distribution.a. What percentage of returns were greater than 20 percent?b. What percentage of returns were below –16 percent?
An investment strategy has an expected return of 8 percent and a standard deviation of 6 percent. Assume investment returns are bell shaped.a. How likely is it to earn a return between 2 percent and 14 percent?b. How likely is it to earn a return greater than 14 percent?c. How likely is it to
Average talk time between charges of a given cell phone is advertised as 4 hours. Let the standard deviation be 0.8 hour.a. Use Chebyshev’s theorem to approximate the proportion of cell phones that will have talk time between 2.4 hours and 5.6 hours.b. Assume a bell-shaped distribution to
Go to the text website and access the data labeled Census. It shows, among other variables, median household income and median house value for the 50 states in 2010. Assume that income and house value data are bell-shaped.a. Use z-scores to determine if there are any outliers in the household
Go to the text website and access the data labeled Fidelity_Select. It shows the annual return (in percent) for the Fidelity Select Technology Fund and the Fidelity Select Energy Fund from 2000 through 2011. Assume that the return data are bell-shaped.a. Use z-scores to determine if there are any
Consider the following frequency distribution.Class .....Frequency2 up to 4 ...204 up to 6 ...606 up to 8 ...808 up to 10 ....20a. Calculate the population mean.b. Calculate the population variance and the population standard deviation.
Consider the following frequency distribution. Class ....... Frequency50 up to 60 .... 1060 up to 70 .... 1570 up to 80 ..... 880 up to 100 .... 2a. Calculate the sample mean.b. Calculate the sample variance and the sample standard deviation.
The following relative frequency distribution was constructed from a population of 200. Calculate the population mean, the population variance, and the population standard deviation.Class .... Relative Frequency220 up to 210 ... 0.35210 up to 0 ..... 0.250 up to 10 ..... 0.4010 up to 20 ..... 0.05
The following relative frequency distribution was constructed from a sample of 50.Class ....Relative Frequency0 up to 2 ...0.342 up to 4 ...0.204 up to 6 ...0.406 up to 8 ..0.06a. Calculate the sample mean, b. Calculate ample variance, and the sample standard deviation.
Fifty cities provided information on vacancy rates (in percent) for local apartments in the following frequency distribution.Vacancy Rate (in percent) ......Frequency0 up to 3 .............. 53 up to 6 .............. 56 up to 9 ..............109 up to 12 .............2012 up to 15 ............10a.
A local hospital provided the following frequency distribution summarizing the weights of babies delivered over the month of January.Weight (in pounds) .... Number of Babies2 up to 4 ........ 34 up to 6 ........ 86 up to 8 ......... 258 up to 10 ....... 3010 up to 12 ........ 4 a. Calculate
A researcher conducts a mileage economy test involving 80 cars. The frequency distribution describing average miles per gallon (mpg) appears in the accompanying frequency distribution.Average MPG ....Frequency15 up to 20 ......1520 up to 25 .......3025 up to 30 .....1530 up to 35 ......1035 up to
The Boston Security Analysts Society, Inc. (BSAS) is a non-profit association that serves as a forum for the exchange of ideas for the investment community. Suppose the ages of its members are based on the following frequency distribution.Age ........Frequency21–31 ........1132–42
The National Sporting Goods Association (NSGA) conducted a survey of the ages of people that purchased athletic footwear in 2009. The ages are summarized in the following relative frequency distribution.Age of Purchaser ...PercentUnder 14 years old ....1914 to 17 years old ..... 618 to 24 years old
Consider the following sample data:a. Calculate the covariance between the variables.b. Calculate and interpret the correlationcoefficient.
Consider the following sample data:a. Calculate the covariance between the variables.b. Calculate and interpret the correlationcoefficient.
The following table shows the annual returns (in percent) for T-Rowe Price’s Value and International Stock funds for the time period 2005–2009.a. Calculate and interpret the covariance between the returns.b. Calculate and interpret the correlationcoefficient.
In an attempt to determine whether a linear 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.a. Calculate the covariance. What kind of linear relationship exists?b.
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 10 students who graduated
A social scientist wants to analyze the relationship between educational attainment and salary. He collects the following sample of data where Education refers to years of higher education and Salary is the person€™s annual salary in thousands of dollars.a. Calculate the covariance. What
a. Compute and interpret the correlation coefficient of household income and house value.b. Compute and interpret the correlation coefficient of household income and the percentage of the residents who are foreign born.c. Compute and interpret the correlation coefficient of household income and the
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). Consider the following table for data on a
Annual growth rates for individual firms in the toy industry tend to fluctuate dramatically, depending on consumers€™ tastes and current fads. Consider the following growth rates (in percent) for two companies in this industry, Hasbro and Mattel.a. Use the standard deviation to evaluate
The following table shows the annual returns (in percent) for Fidelity’s Electronic and Utilities funds.a. Calculate the sample mean, the sample variance, and the sample standard deviation for each fund.b. Which fund had the higher average return?c. Which fund was riskier over this time
Monthly stock prices for two competing firms are as follows.a. Calculate the sample mean, the sample variance, and the sample standard deviation for each firm€™s stock price.b. Which firm had the higher stock price over the time period?c. Which firm€™s stock price had greater
The manager at a water park constructed the following frequency distribution to summarize attendance for 60 days in July and August.Attendance ......Frequency1,000 up to 1,250 ..... 51,250 up to 1,500 ..... 61,500 up to 1,750 .....101,750 up to 2,000 .....202,000 up to 2,250 .....152,250 up to
The National Sporting Goods Association (NSGA) conducted a survey of the ages of individuals that purchased skateboarding footwear. The ages of this survey are summarized in the following relative frequency distribution.Age of User ........PercentUnder 14 years old .....3514 to 17 years old
The following table shows the annual returns (in percent) for two of Putnam’s mutual funds: the Voyager Growth Fund and the George Putnam Fund of Boston.a. Calculate and interpret the covariance.b. Calculate the correlation coefficient. Comment on the strength of the linearrelationship.
A manager of a local retail store analyzes the relationship between advertising and sales by reviewing the store’s data for the previous six months.Advertising (in $100s) ....Sales (in $1,000s)20 ............1525 ............1830 ............2022 ............1627 ............1926 ............20a.
An economist wishes to summarize sample data from 26 metropolitan areas in the United States. The following table lists a portion of each area€™s 2010€“2011 median income as well as the monthly unemployment rate and average consumer debt for August 2010; the entire data set,
American football is the highest paying sport on a per-game basis. Given that the quarterback is considered the most important player on an NFL team, he is typically well-compensated. Consider a portion of the following quarterback salary data in 2009; the entire data set, labeled Quarterback
The accompanying table shows a portion of the number of cases of car thefts for the 50 states during 2010. The entire data set, labeled Car_Theft, can be found on the text website.State ..... Car TheftAlabama .... 658Alaska ..... 280: :Wyoming .... 84a. Calculate the mean, the median, and the
The accompanying table shows a portion of the average price for a gallon of gas for the 50 states during April 2012. The entire data set, labeled Gas_Prices_2012, can be found on the text website.State ....Price per GallonAlabama ....$4.36Alaska .... 3.79: :Wyoming ... 3.63a. Construct a box-plot
The accompanying table shows a portion of the number of cases of crime related to gambling (Gambling) and offenses against the family and children (Family Abuse) for the 50 states in the United States during 2010. The entire data set, labeled Gambling, can be found on the text website.a. Construct
Given the following observations from a population, calculate the mean, the median, and themode.
An investor bought common stock of Microsoft Corporation on three occasions at the following prices.Calculate the average price per share at which the investor bought these shares.
Consider the following box plot.a. Does the above box plot indicate possible outliers in the data?b. Comment on the the skewness of the underlyingdistribution.
Consider the following box plot.a. Does the above box plot indicate possible outliers in the data?b. Comment on the skewness of the underlyingdistribution.
Consider a bell-shaped distribution with a mean of 750 and a standard deviation of 50. There are 500 observations in the data set.a. What percentage of the observations are less than 700?b. Approximately how many observations are less than 700?
Data are drawn from a bell-shaped distribution with a mean of 25 and a standard deviation of 4. There are 1,000 observations in the data set.a. What percentage of the observations are less than 33?b. Approximately how many observations are less than 33?
Data with 250 observations are drawn from a bell-shaped distribution with a mean of 50 and a standard deviation of 12. Approximately how many observations are more than 74?
Consider a sample with six observations of 6, 9, 12, 10, 9, and 8. Compute the z-scores for each sample observation.
It is often assumed that IQ scores follow a bell-shaped distribution with a mean of 100 and a standard deviation of 16.a. What percentage of scores are between 84 and 116?b. What percentage of scores are less than 68?c. What percentage of scores are more than 116?
The following table lists the sales (in millions of dollars) of the top Italian restaurant chains in 2009.Restaurant ......... Sales (millions)Olive Garden ......... $3,300Carrabba’s Italian Grill ..... 629Romano’s Macaroni Grill ..... 583Maggiano’s .......... 366Carino’s
An article in The Wall Street Journal (July 11, 2008) outlined a number of reasons as to why the 16 teams in Major League Baseball’s National League (NL) are inferior to the 14 teams in the American League (AL). One reason for the imbalance pointed to the disparity in opening-day payrolls:
Five years after graduating from college, Lucia Li feels that she is finally ready to invest some of her earnings. She has eliminated her credit card debt and has established an emergency fund. Her parents have been pleased with the performance of their mutual fund investments with Janus Capital
Due to a crisis in subprime lending, obtaining a mortgage has become difficult even for people with solid credit. In a report by the Associated Press (August 25, 2007), sales of existing homes fell for a 5th consecutive month, while home prices dropped for a record 12th month in July 2007.
Consider the following data:x̅1 = 25.7 x̅2 = 30.6σ21 = 98.2 σ 22 = 87.4n1 = 20 n2 = 25a. Construct a 95% confidence interval for the difference between the population means.b.
Consider the following data:a. Construct a 95% confidence interval for the difference between the population means. Assume the population variances are unknown but equal.b. Specify the competing hypotheses in order to determine whether or not the population means differ.c. Using the confidence
Consider the following competing hypotheses and accompanying sample data drawn independently from normally distributed populations.a. Using the p -value approach, test whether the population means differ at the 5% significance level.b. Repeat the hypothesis test using the critical value approach.
Consider the following competing hypotheses and accompanying sample data. The two populations are known to be normally distributed.H0: µ1 - µ2 ≤ 0HA: µ1 - µ2 > 01 = 20.2 2 = 17.5s1 = 21.5 s2 = 15.2n1 = 22 n2 = 18a. Implement the test at the 5% level under the assumption that the
Consider the following competing hypotheses and accompanying sample data drawn independently from normally distributed populations.H0: µ1 - µ2 ≤ 0HA: µ1 - µ2 > 01 = 249 2 = 272s1 = 35 s2 = 23n1 = 10 n2 = 10a. Implement the test at the 5% level under the assumption that the population
Consider the following competing hypotheses and accompanying sample data.H0: µ1 - µ2 = 0HA: µ1 - µ2 ≠ 01 = 57 2 = 43s1 = 21.5 s2 = 15.2n1 = 22 n2 = 18Assume that the populations are normally distributed with unknown but equal variances.a. Calculate the value of the test statistic.b.
Consider the following sample data drawn independently from normally distributed populations with equal population variances.Sample 1Sample
Consider the following sample data drawn independently from normally distributed populations with unequal population variances.Sample 1 Sample 288........... 98110...........114102...........11896...........12874...........102120...........110a. Construct the relevant hypothesis to test if the
According to a new Health of Boston report, female residents in Boston have a higher average life expectancy as compared to male residents (The Boston Globe, August 16, 2010). You collect the following sample data to verify the results of the report. You also use the historical standard deviation
A joint project of the U.S. Census Bureau and the National Science Foundation shows that people with a bachelor’s degree who transferred from a community college earn less than those who start at a four-year school (USA TODAY, March 17, 2009). Previous studies referred to this occurrence as a
The Chartered Financial Analyst (CFA®) designation is fast becoming a requirement for serious investment professionals. It is an attractive alternative to getting an MBA for students wanting a career in investment. A student of finance is curious to know if a CFA designation is a more lucrative
A phone manufacturer wants to compete in the touch screen phone market. Management understands that the leading product has a less than desirable battery life. They aim to compete with a new touch phone that is guaranteed to have a battery life more than two hours longer than the leading product. A
In May 2008, CNN reported that sports utility vehicles (SUVs) are plunging toward the “endangered” list. Due to soaring oil prices and environmental concerns, consumers are replacing gas-guzzling vehicles with fuel-efficient smaller cars. As a result, there has been a big drop in the demand for
A consumer advocate researches the length of life between two brands of refrigerators, Brand A and Brand B. He collects data (measured in years) on the longevity of 40 refrigerators for Brand A and repeats the sampling for Brand B. The data set, labeled Refrigerator_Longevity, can be found on the
According to a study published in the New England Journal of Medicine, overweight people on low-carbohydrate and Mediterranean diets lost more weight and got greater cardiovascular benefits than people on a conventional low-fat diet (Boston Globe, July 17, 2008). A nutritionist wishes to verify
Baseball has always been a favorite pastime in America and is rife with statistics and theories. In a recent paper, researchers showed that major league players who have nicknames live 2½ years longer than those without them (The Wall Street Journal, July 16, 2009). You do not believe in this
As the class of 2012 celebrates the end of college, for many the promise of a college degree has turned to disappointment as they find themselves struggling to find a job (Financial Times, June 1, 2012). It is especially disturbing since recent evidence suggests that graduating at bad economic
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
A sample of 20 paired observations generates the following data: d̅ = 1.3 and sD2 = 2.6. Assume a normal distribution.a. Construct a 90% confidence interval for the mean difference µD .b. Using the confidence interval, test whether the mean difference differs from zero. Explain.
The following table contains information on matched sample values whose differences are normally distributed.a. Construct a 95% confidence interval for the mean difference µD .b. Specify the competing hypotheses in order to test whether the mean difference differs from zero.c. Using the
Consider the following competing hypotheses and accompanying results from matched samples:H0: µD ≥ 0; HA: µD < 0d̅ = 22.8 , sD = 5.7 , n = 12a. At the 5% significance level, find the critical value(s).b. Calculate the value of the test statistic under the assumption that the sample
A sample of 35 paired observations generates the following results: d̅ = 1.2 and sD = 3.8.a. Specify the appropriate hypotheses to test if the mean difference is greater than zero.b. Compute the value of the test statistic and approximate the p-value.c. At the 5% significance level, can you
Consider the following matched samples representing observations before and after an experiment. Assume that the sample differences are normally distributed.a. Construct the competing hypotheses to determine if the experiment increases the magnitude of the observations.b. Implement the test at a 5%
A manager of an industrial plant asserts that workers on average do not complete a job using Method A in the same amount of time as they would using Method B. Seven workers are randomly selected. Each worker’s completion time (in minutes) is recorded by the use of Method A and Method B.a.
A diet center claims that it has the most effective weight loss program in the region. Its advertisements say, “Participants in our program lose more than 5 pounds within a month.â€Six clients of this program are weighed on the first day of the diet and then one month later.a. Specify
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 evaluates six properties that the appraisers had valued recently.a. Specify the competing
A recent report criticizes SAT-test-preparation providers for promising big score gains without any hard data to back up such claims (The Wall Street Journal, May 20, 2009). Suppose eight college-bound students take a mock SAT, complete a three-month test-prep course, and then take the real SAT.
The following table shows the annual returns (in percent) for Fidelity’s Select Electronic and Select Utilities mutual funds. The data set, labeled Electronic_Utilities, can also be found on the text website.a. Set up the hypotheses to test the claim that the mean return for the Electronic
It is fairly common for people to put on weight when they quit smoking. While a small weight gain is normal, excessive weight gain can create new health concerns that erode the benefits of not smoking. The accompanying table shows a portion of the weight data for 50 women before quitting and six
When faced with a power hitter, many baseball teams utilize a defensive shift. A shift usually involves putting three infielders on one side of second base against pull hitters. Many believe that a power hitter’s batting average is lower when he faces a shift defense as compared to when he
A random sample of five observations from three normally distributed populations produced the following data:a. Calculate the grand mean.b. Calculate SSTR and MSTR.c. Calculate SSE and MSE.d. Specify the competing hypotheses in order to determine whether some differences exist between the
Random sampling from four normally distributed populations produced the following data:a. Calculate the grand mean.b. Calculate SSTR and MSTR .c. Calculate SSE and MSE .d. Specify the competing hypotheses in order to determine whether some differences exist between the population means.e. Calculate
Given the following information obtained from three normally distributed populations, construct an ANOVA table and perform an ANOVA test of mean differences at the 1% significance level.SSTR = 220.7; SSE = 2,252.2; c = 3; n1 = n2 = n3 = 8
Given the following information obtained from four normally distributed populations, construct an ANOVA table and perform an ANOVA test of mean differences at the 5% significance level. SST = 70.47; SSTR = 11.34; c = 4; n1 = n2 = n3 = n4 = 15
An analysis of variance exp experiment produced a portion of the accompanying ANOVA table.a. Fill in the missing statistics in the ANOVA table.b. Specify the competing hypotheses in order to determine whether some differences exist between the population means.c. At the 5% significance level, what
An analysis of variance experiment produced a portion of the following ANOVA table.a. Fill in the missing statistics in the ANOVA table.b. Specify the competing hypotheses in order to determine whether some differences exist between the population means.c. At the 10% significance level, what is the
Asian residents in Boston have the highest average life expectancy of any racial or ethnic group—a decade longer than black residents (Boston Globe, August 16, 2010). Suppose sample results indicative of the overall results are as follows.a. Construct an ANOVA table. Assume life expectancies
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 brands of detergents, 24 swatches of white cloth were soiled with red wine and grass stains and then washed in front-loading
A recent survey by Genworth Financial Inc., a financial-services company, concludes that the cost of long-term care in the United States varies significantly, depending on where an individual lives (The Wall Street Journal, May 16, 2009). An economist collects data from the five states with the
An online survey by the Sporting Goods Manufacturers Association, a trade group of sports retailers and marketers, claimed that household income of recreational athletes varies by sport (The Wall Street Journal, August 10, 2009). In order to verify this claim, an economist samples five sports
Do energy bills vary dramatically depending on where you live in the United States? Suppose 25 households from four regions in the United States are sampled. The values for the average annual energy bill are shown in the accompanying table and are consistent with those found byThe Department of
The accompanying table shows a portion of quarterly data on Nike’s revenue for the fiscal years 2001 through 2010. Data for Nike’s fiscal year refer to the time period from June 1 through May 31. The entire data set, labeled Nike_Revenues, can be found on the text website.Assume
The accompanying table shows a portion of the number of customers that frequent a restaurant on weekend days over the past 52 weeks. The entire data set, labeled Patronage, can be found on the text website.At the 5% significance level, can we conclude that the average number of customers that
A human resource specialist wants to determine whether the average job satisfaction score (on a scale of 0 to 100) differs depending on a person’s field of employment. She collects scores from 30 employees in three different fields. A portion of the data is shown in the accompanying table.
Do men really spend more money on St. Patrick’s Day as compared to women? A recent survey found that men spend an average of $43.87 while women spend an average of $29.54 (USA Today, March 17, 2009). Assume that these data were based on a sample of 100 men and 100 women and the population
A new study has found that, on average, 6- to 12-year-old children are spending less time on daily household chores today compared to 1981 levels (The Wall Street Journal, August 27, 2008). Suppose two samples representative of the study’s results report the following summary statistics for the
Paige Thomsen is about to graduate from college at a local university in San Francisco. Her options are to look for a job in San Francisco or go home to Denver and search for work there. Recent data suggest that average starting salaries for college graduates is $48,900 in San Francisco and $40,900
It is well documented that cholesterol over 200 is a risk factor in developing heart disease for both men and women. Younger men are known to have higher cholesterol levels than younger women; however, beyond age 55, women are more likely to have higher cholesterol levels. A recent college graduate
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