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business statistics communicating
Business Statistics Communicating With Numbers 1st Edition Kelly Jaggia - Solutions
Executive compensation has risen dramatically beyond the rising levels of an average worker's w age over the years.Sarah is an MBA student who decides to use her statistical skills to estimate the mean CEO compensation in 2010 for all large companies in the United States. She takes a random sample
A price-earnings ratio or P/E ratio is calculated as a firm's share price compared to the income or profit earned by the firm per share. Generally, a high P/E ratio suggests that investors are expecting higher earnings growth in the future compared to companies with a lower P/E ratio. The following
The monthly closing stock prices (rounded to the nearest dollar) for Panera Bread Co. for the first six months of 2010 are reported in the following table.a. Calculate the sample mean and the sample standard deviation.b. Compute the 90% confidence interval of the mean stock price of Panera Bread
A recent study found that consumers are making average monthly debt payments of $983 (Experian.com, November 11 , 2010). The accompanying table shows a portion of average debt payments for 26 metropolitan areas. The complete data set is on the text website and is labeled D e b t Paym ents.City Debt
A random sample of 100 observations results in 40 successes.a. What is the point estimate of the population proportion of successes?b. Construct a 90% confidence interval of the population proportion.c. Construct a 99% confidence interval of the population proportion. P-69
A random sample of 80 observations results in 50 successes.a. Construct a 95% confidence interval of the population proportion of successes.b. Construct a 95% confidence interval of the population proportion of failures. P-69
Assume in a sample size of n = 50.a. Construct a 95% confidence interval of the population proportion.b. What happens to the margin of error if the above sample proportion is based on n = 200 instead of n = 50? P-69
A sample of 80 results in 30 successes.a. Calculate the point estimate of the population proportion of successes.b. Construct a 90% and a 99% confidence interval of the population proportion.c. Can w e conclude at 90% confidence that the population proportion differs from 0.5?d. Can w e conclude at
In a sample of 30 observations the number of successes equals 18.a. Construct an 88% confidence interval of the population proportion of successes.b. Construct a 98% confidence interval of the population proportion of successes.c. What happens to the margin of error as you move from an 88%
A survey of 1,026 people asked: "What would you do with an unexpected tax refund?" Forty-seven percent responded that they would pay off debts (Vanity Fair, June 2010).a. At 95% confidence, what is the margin of error?b. Construct a 95% confidence interval of the population proportion of people who
A recent poll of 1,079 adults finds that 51% of Americans support Arizona's stringent new immigration enforcement law, even though it may lead to racial profiling (New York Times/CBS News, April 28-May 2 , 2010). Use the sample information to compute a 95% confidence interval of the population
An economist reports that 560 out of a sample of 1,200 middle-income American households actively participate in the stock market.a. Construct a 90% confidence interval of the proportion of middle-income Americans who actively participate in the stock market.b. Can we conclude that the proportion
In a CNNMoney.com poll conducted on July 1 3 , 2010, a sample of 5,324 Americans were asked about what matters most to them in a place to live. Thirty-seven percent of the respondents felt job opportunities matter most.a. Construct a 90% confidence interval of the proportion of Americans who feel
In a recent poll of 760 homeowners in the United States, one in five homeowners report having a home equity loan that they are currently paying off. Using a confidence coefficient of 0.90, derive an interval estimate of the proportion of all homeowners in the United States that hold a home equity
In an NBC News/Wall Street Journal poll of 1,000 American adults conducted on August 5–9 , 2 0 1 0 , 44% of respondents approved of the job that Barack Obama was doing in handling the economy.a. Compute a 90% confidence interval of the proportion of Americans who approved of Barack Obama's
Obesity is generally defined as 30 or more pounds over a healthy weight. A recent study of obesity reports 27.5% of a random sample of 400 adults in the United States to be obese.a. Use this sample information to compute a 90% confidence interval of the adult obesity rate in the United States.b. Is
An accounting professor is notorious for being stingy in giving out good letter grades. In a large section of 140 students in the fall semester, she gave out only 5% As, 23% Bs, 42% Cs, and 30% Ds and Fs. Assuming that this was a representative class, compute a 95% confidence interval of the
One in five 18-year-old Americans has not graduated from high school (The Wall Street Journal, April 19 , 2007). A mayor of a northeastern city comments that its residents do not have the same graduation rate as the rest of the country. An analyst from the Department of Education decides to test
What is the minimum sample size n required to estimateµ with 90% confidence if the desired margin of error is D = 1.2? The population standard deviation is estimated What happens to n if the desired margin of error decreases to D = 0.7? P-69
The lowest and highest observations in a population are 20 and 80, respectively. What is the minimum sample size n required to estimate µ with 80% confidence if the desired margin of error is D = 2.6? What happens to n if you decide to estimate µ with 95% confidence? P-69
You need to compute a 99% confidence interval of the population mean. How large a sample should you draw to ensure that the sample mean does not deviate from the population mean by more than 1.2? (Use 6.0 as an estimate of the population standard deviation from prior studies.) P-69
What is the minimum sample size n required to estimate p with 95% confidence if the desired margin of error D = 0.08?The population proportion is estimated as prior studies. What happens to n if the desired margin of error increases to D = 0.12? P-69
In the planning stage, a sample proportion is estimated as Use this information to compute the minimum sample size n required to estimate p with 99% confidence if the desired margin of error D = 0.12.What happens to n if you decide to estimate p with 90%confidence? P-69
You wish to compute a 95% confidence interval of the population proportion. How large a sample should you draw to ensure that the sample proportion does not deviate from the population proportion by more than 0.06? No prior estimate of the population proportion is available. P-69
An analyst from an energy research institute in California wishes to precisely estimate a 99% confidence interval of the average price of unleaded gasoline in the state. In particular, she does not want the sample mean to deviate from the population mean by more than $0.06. What is the minimum
An analyst would like to construct 95% confidence intervals of the mean returns of two mutual funds. Fund A is a highrisk fund with a known population standard deviation of 20.6%, whereas the Fund B is a lower-risk fund with a known population standard deviation of 12.8%.a. What is the minimum
The manager of a pizza chain in Albuquerque, New Mexico, wants to determine the average size of their advertised 16-inch pizzas. She takes a random sample of 25 pizzas and records their mean and standard deviation as 16.10 and 1.8 inches, respectively. She subsequently computes a 95%confidence
Mortgage lenders often use FICO® scores to check the credit worthiness of consumers applying for real estate loans.In general, FICO scores range between 300 and 850 with higher scores representing a better credit profile. A lender in a Midwestern town would like to estimate the mean credit score
A student of business is interested in estimating a 99%confidence interval of the proportion of students who bring laptops to campus. He wishes a precise estimate and is willing to draw a large sample that will keep the sample proportion within five percentage points of the population proportion.
Over a 10-year sample period, the mean return and standard deviation of annual returns on a portfolio you are analyzing were 10% and 15%, respectively. You assume that returns are normally distributed. Construct a 95% confidence interval of the population mean. P-69
A realtor in Mission Viejo, California, wants to estimate the average price of a house in the city.a. Open the Mission Viejo (raw) data from the text website into an Excel spreadsheet (data are in $1,000s). Assume the population standard deviation is $100 (in $1,000s).b. Construct a 90% and a 99%
A hair salon in Cambridge, Massachusetts, reports that on seven randomly selected weekdays, the number of customers who visited the salon were 40, 3 0 , 2 8 , 2 2 , 3 6 , 16, and 50. It can be assumed that weekday customer visits follow a normal distribution.a. Construct a 90% confidence interval
Recently, six single-family homes in San Luis Obispo County in California sold at the following prices (in $1,000s): $549,$449, $705, $529, $639, $609.a. Construct a 95% confidence interval for the mean sale price in San Luis Obispo County.b. What assumption have you made when constructing this
According to data from the Organization for Economic Cooperation and Development, the average U.S. worker takes 16 days of vacation each year (The Wall Street Journal, June 2 0 , 2007). Assume that these data were based on a sample of 225 workers and that the sample standard deviation is 12 days.a.
A machine that is programmed to package 1.20 pounds of cereal is being tested for its accuracy. In a sample of 36 cereal boxes, the sample mean filling weight is calculated as 1.22 pounds. The population standard deviation is known to be 0.06 pound.a. Identify the relevant parameter of interest for
A recent study by Allstate Insurance Co. finds that 82% of teenagers have used cell phones while driving (The Wall Street Journal, May 5 , 2010). Suppose this study was based on a random sample of 50 teen drivers.a. Construct a 99% confidence interval for the proportion of all teenagers that have
The following table shows the annual returns (in percent)for the Vanguard Energy Fund.a. Calculate the point estimate for µ .b. Construct a 95% confidence interval for µ .c. What assumption did you make when constructing the interval? P-69 Year Return 2005 44.60 2006 19.68 2007 37.00 2008 -42.87
While the housing market is in the tank and is not likely to emerge anytime soon, real estate investment in college towns continues to promise good returns (The Wall Street Journal, September 2 4 , 2010). Marcela Treisman works for an investment firm in Michigan. Her assignment is to analyze the
According to a survey of 1,235 businesses by IDC, a marketresearch concern in Framingham, Massachusetts, 12.1% of sole proprietors are engaging in e-commerce (The Wall Street Journal, July 2 6 , 2007).a. What is the margin of error in estimating with 95%confidence the proportion of sole proprietors
A Monster.com poll of 3,057 individuals asked: "What's the longest vacation you plan to take this summer?" The following relative frequency distribution summarizes the results.Response Relative Frequency A few days 21%A few long weekends 18%One week 36%Two weeks 22%Source: The Boston Globe, June
The precision of a confidence interval is directly linked with the width of the interval:the wider the interval, the lower is its precision. A confidence interval is wider (a) the greater the population standard deviation σ , (b) the smaller the sample size n, and(c) the greater the confidence
The t distribution is a family of distributions that are similar to the z distribution, in that they are all symmetric and bell-shaped around zero with asymptotic tails.However, the t distribution has broader tails than does the z distribution. Each t distribution is identified by a parameter known
Over a 10-year sample period, the mean return and standard deviation of annual returns on a portfolio you are analyzing were 10% and 15%, respectively. You assume that returns are normally distributed. Construct a 95% confidence interval of the population mean. P-69
A realtor in Mission Viejo, California, wants to estimate the average price of a house in the city.a. Open the Mission Viejo (raw) data from the text website into an Excel spreadsheet (data are in $1,000s). Assume the population standard deviation is $100 (in $1,000s).b. Construct a 90% and a 99%
Percentiles provide detailed information about how the data are spread over the interval from the smallest value to the largest value. In general, the pth percentile divides the data set into two parts, where approximately p percent of the observations have values less than the pth percentile and
You score 90 on the midterm, 60 on the final, and 80 on the class project. What is your average score if the midterm is worth 30%, the final is worth 50% and the class project is worth 20%? R-96
Average talk time between charges of a given cell phone is advertised as 4 hours. Let the standard deviation be 0.8 hours.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
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 earn
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? R-96
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?
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
Data with 250 observations are drawn from a relatively symmetric and bell-shaped distribution with a mean of 50 and a range of 48.a. What is the rough estimate of the standard deviation?b. Approximately how many observations are more than 74? R-96
A hair salon in Cambridge, Massachusetts, reports that on seven randomly selected weekdays, the number of customers who visited the salon were 40, 3 0 , 2 8 , 2 2 , 3 6 , 16, and 50. It can be assumed that weekday customer visits follow a normal distribution.a. Construct a 90% confidence interval
Data are drawn from a relatively symmetric and bell-shaped distribution with a mean of 5 and a range of 10.a. What is the rough estimate of the standard deviation?b. What percentage of the observations are positive?c. What percentage of the observations are not positive? R-96
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?50. Data are drawn from a symmetric and bell-shaped distribution with a mean of 25 and a standard deviation of 4.There are 1000 observations
Consider a symmetric and bell-shaped distribution with a mean of 750 and a standard deviation of? R-96
Data are drawn from a relatively symmetric and 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
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. R-96
A data set has a mean of 1500 and a standard deviation of 100.a. Using Chebyshev's Theorem, what percentage of the observations fall between 1300 and 1700?b. Using Chebyshev's Theorem, what percentage of the observations fall between 1100 and 1900? R-96
A data set has a mean of 80 and a standard deviation of 5.a. Using Chebyshev's Theorem, what percentage of the observations fall between 70 and 90?b. Using Chebyshev's Theorem, what percentage of the observations fall between 65 and 95? R-96
FILE Go to the text website and access the data labeled Largest Corporations. It shows the Fortune 500 rankings of America's largest corporations for 2010. Next to each corporation are its market capitalization (in billions of dollars as of March 26 , 2010) and its total return to investors for the
The returns for an auto firm are 5% in Year 1 and 3% in the first quarter o f Year 2. Calculate the annualized return for the period. R-96
Recently, six single-family homes in San Luis Obispo County in California sold at the following prices (in $1,000s): $549,$449, $705, $529, $639, $609.a. Construct a 95% confidence interval for the mean sale price in San Luis Obispo County.b. What assumption have you made when constructing this
The returns from an investment are 2% in Year 1,5% in Year 2, and 1.8% in the first half o f Year 3. Calculate the annualized return for the entire period. R-96
The returns for a pharmaceutical firm are 10% in Year 1,5%in Year 2, and – 15% in Year 3. What is the annualized return for the period? R-96
Use the data in Table 3.1 to calculate the geometric mean for the Metals and the Income funds? R-96
The geometric mean is a multiplicative average, as opposed to an additive average(the arithmetic mean). It is the relevant measure when evaluating investment returns over several years. It is also the relevant measure when calculating average growth rates. R-96
Consider the return data (in percent) for the Income fund in Table 3,1,a. Calculate and interpret the 25th, 50th, and 75th percentiles.b. Construct a box plot. Are there any outliers?c. Is the distribution symmetric? If not, comment on its skewness. R-96
Consider the information presented in the introductory case of this chapter. Calculate and interpret the 25th and the 75th percentiles for the Metals fund. R-96
According to data from the Organization for Economic Cooperation and Development, the average U.S. worker takes 16 days of vacation each year (The Wall Street Journal, June 2 0 , 2007). Assume that these data were based on a sample of 225 workers and that the sample standard deviation is 12 days.a.
The following table shows a portion of the sale price (in$ 1000s) for 36 homes sold in Mission Viejo, CA, during June 2010; the complete data, labeled Mission Viejo Houses, are also available on the text website. R-96 Number Sale Price (in $1000s)1 $430 2 520⋮ ⋮36 430a. Calculate the mean, the
Use the data in Table 3.2 to calculate the mode salary of employees at Acetech. R-69
Let’s use the data in Table 3.1 in the introductory case to calculate and interpret the mean return of the Metals fund and the mean return of the Income fund. R-69
Calculate and interpret the covariance and the correlation coefficient. R-69
Calculate the mean and the variance for grouped data. R-69
Apply Chebyshev's Theorem and the empirical rule.
Explain mean-variance analysis and the Sharpe ratio. R-69
Calculate and interpret the range, the mean absolute deviation, the variance, the standard deviation, and the coefficient of variation. R-69
Calculate and interpret a geometric mean return and an average growth rate. R-69
A machine that is programmed to package 1.20 pounds of cereal is being tested for its accuracy. In a sample of 36 cereal boxes, the sample mean filling weight is calculated as 1.22 pounds. The population standard deviation is known to be 0.06 pound.a. Identify the relevant parameter of interest for
Calculate and interpret percentiles and a box plot. R-69
Calculate and interpret the arithmetic mean, the median, and the mode. R-69
A recent study by Allstate Insurance Co. finds that 82% of teenagers have used cell phones while driving (The Wall Street Journal, May 5 , 2010). Suppose this study was based on a random sample of 50 teen drivers.a. Construct a 99% confidence interval for the proportion of all teenagers that have
The following table shows the annual returns (in percent)for the Vanguard Energy Fund. P-69a. Calculate the point estimate for µ .b. Construct a 95% confidence interval for µ .c. What assumption did you make when constructing the interval? Year Return 2005 44.60 2006 19.68 2007 37.00 2008 -42.87
While the housing market is in the tank and is not likely to emerge anytime soon, real estate investment in college towns continues to promise good returns (The Wall Street Journal, September 2 4 , 2010). Marcela Treisman works for an investment firm in Michigan. Her assignment is to analyze the
According to a survey of 1,235 businesses by IDC, a marketresearch concern in Framingham, Massachusetts, 12.1% of sole proprietors are engaging in e-commerce (The Wall Street Journal, July 2 6 , 2007).a. What is the margin of error in estimating with 95%confidence the proportion of sole proprietors
A Monster.com poll of 3,057 individuals asked: "What's the longest vacation you plan to take this summer?" The following relative frequency distribution summarizes the results. P-69a. Construct a 95% confidence interval for the proportion of people who plan to take a one-week vacation this
Recall Example 8.6, where Jared Beane wants to construct a 90% confidence interval of the proportion of all ultra-green cars that obtain over 100 mpg. Jared does not want the margin of error to be more than 0.10. How large a sample does Jared need for his analysis of the population proportion?
Let us revisit Example 8.5, where Jared Beane wants to construct a 90% confidence interval of the mean mpg of all ultra-green cars. Suppose Jared would like to constrain the margin of error to within 2 mpg. Further, Jared knows that the lowest mpg in the population is 76 mpg, whereas the highest is
In the introductory case of this chapter, Jared Beane wants to estimate the mean mpg of all ultra-green cars. Table 8.1 lists the mpg of a sample of 25 cars. Use this information to construct a 90% confidence interval of the population mean. Assume that mpg follows a normal distribution. P-69
IQ tests are designed to yield results that are approximately normally distributed. Researchers think that the population standard deviation is 15. A reporter is interested in estimating the average IQ of employees in a large high-tech firm in California. She gathers the IQ information on 22
Let the standard deviation of the population in Example 8.2 be 0.05 instead of 0.03.Compute a 95% confidence interval based on the same sample information. P-69
A sample of 25 cereal boxes of Granola Crunch, a generic brand of cereal, yields a mean weight of 1.02 pounds of cereal per box. Construct a 95% confidence interval of the mean weight of all cereal boxes. Assume that the weight is normally distributed with a population standard deviation of 0.03
In 2007, 45% of women ages 25 to 34 had a college degree, compared with 36% of young men (The Wall Street Journal, May 29, 2008).a. What is the probability that a randomly selected woman between the ages of 25 to 34 does not have a college degree?b. What is the probability that a randomly selected
Anthony feels that he has a 75% chance of getting an A in Statistics and a 55%chance of getting an A in Managerial Economics. He also believes he has a 40% chance of getting an A in both classes.a. What is the probability that he gets an A in at least one of these courses?b. What is the probability
Samantha Greene, a college senior, contemplates her future immediately after graduation. She thinks there is a 25% chance that she will join the Peace Corps and teach English in Madagascar for the next 27 months. Alternatively, she believes there is a 35% chance that she will enroll in a full-time
What is the probability that a customer is under 35 years of age, given that the customer made an Under Armour purchase? P-258
What is the probability that a customer is either younger than 35 years old or purchases an Under Armour garment? P-258
What is the probability that a customer is younger than 35 years old and purchases an Under Armour garment? P-258
What is the probability that a randomly selected customer purchases an Under Armour garment? P-258
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