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 accompanying table shows a portion of companies that comprise the Dow Jones Industrial Average (DJIA) and their P/E ratios as of May 17, 2012 (at the time data were retrieved, the P/E ratio for Bank of America was not available). Company …………………………………………………………………………. P/E Ratio 3M (MMM) …………………………………………………………………………………. 14 Alcoa (AA) …………………………………………………………………………………. 24 ⋮ …………………………………………………………………………………………………… ⋮ Walt Disney (DIS) …………………………………………………………………………. 14 a. Calculate and interpret the 25th, 50th, and 75th percentiles. b. Construct a boxplot. Are there any outliers? Is the distribution symmetric? If not, comment on its skewness.
> Which sample information in the preceding question enables us to reject the null hypothesis at α = 0.05 and at α = 0.10?
> Which sample information in the preceding question enables us to reject the null hypothesis at α = 0.01 and at α = 0.10?
> According to a report, college graduates in 2010 were likely to face better job prospects than 2009 graduates (The New York Times, May 24, 2010). Many employers who might have been pessimistic at the start of the 2009–2010 academic year were making more
> An article found that Massachusetts residents spent an average of $860.70 on the lottery in 2010, more than three times the U.S. average (www.businessweek.com, March 14, 2012). A researcher at a Boston think tank believes that Massachusetts residents spe
> A police officer is concerned about speeds on a certain section of Interstate 95. The data accompanying this exercise show the speeds of 40 cars on a Saturday afternoon. a. The speed limit on this portion of Interstate 95 is 65 mph. Specify the competing
> A study found that consumers are making average monthly debt payments of $983 (Experian.com, November 11, 2010). The data accompanying this exercise show the average debt payments (Debt, in $) for 26 metropolitan areas, a portion of which is shown in the
> One of the consequences of the Great Recession was a free fall of the stock market’s average price/earnings ratio, or P/E ratio (The Wall Street Journal, August 30, 2010). Generally, a high P/E ratio suggests that investors are expecting higher earnings
> In September 2007, U.S. home prices fell at a record pace, and price declines in Los Angeles and Orange counties in California outpaced other major metropolitan areas (Los Angeles Times, November 28, 2007). The report was based on the Standard & Poor’s/C
> Economists (NABE), the U.S. gross domestic product (GDP) will expand by 3.2% in 2011 (The Wall Street Journal, May 23, 2010). Suppose the sample standard deviation of their predictions was 1%. At the 5% significance level, test if the mean forecast GDP o
> A local brewery wishes to ensure that an average of 12 ounces of beer is used to fill each bottle. In order to analyze the accuracy of the bottling process, the bottler takes a random sample of 48 bottles. The sample mean weight and the sample standard d
> Small, energy-efficient, Internet-centric, new computers are increasingly gaining popularity (The New York Times, July 20, 2008). Some of the biggest companies are wary of the new breed of computers because their low price could threaten PC makersâ
> The manager of a small convenience store does not want her customers standing in line for too long prior to a purchase. In particular, she is willing to hire an employee for another cash register if the average wait time of the customers is more than fiv
> Which of the sample information in the preceding question enables us to reject the null hypothesis at α = 0.01 and at α = 0.10?
> Executive compensation has risen dramatically compared to the rising levels of an average worker’s wage 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 companie
> Which of the sample information in the preceding question enables us to reject the null hypothesis at α = 0.01 and at α = 0.10?
> On average, a college student graduates with $27,200 in debt (The Boston Globe, May 27, 2012). A researcher collects data on debt from 40 recent undergraduates from Connecticut. Assume that the population standard deviation is $5,000. a. The researcher b
> A realtor in Mission Viejo, California, believes that the average price of a house is more than $500,000. a. State the null and the alternative hypotheses for the test. b. The data accompanying this exercise show house prices. (Data are in $1,000s.) c. A
> A local bottler in Hawaii wishes to ensure that an average of 16 ounces of passion fruit juice is used to fill each bottle. In order to analyze the accuracy of the bottling process, he takes a random sample of 48 bottles. The mean weight of the passion f
> In May 2008, CNN reported that sports utility vehicles (SUVs) are plunging toward the “endangered” list. Due to the uncertainty of oil prices and environmental concerns, consumers are replacing gas-guzzling vehicles with fuel-efficient smaller cars. As a
> It is advertised that the average braking distance for a small car traveling at 65 miles per hour equals 120 feet. A transportation researcher wants to determine if the statement made in the advertisement is false. She randomly test drives 36 small cars
> The sudoku puzzle has become very popular all over the world. It is based on a 9 × 9 grid and the challenge is to fill in the grid so that every row, every column, and every 3 × 3 box contains the digits 1 through 9. A researcher is interested in estimat
> Consider the following hypotheses: A sample of 25 observations yields a sample mean of 13.4. Assume that the sample is drawn from a normal population with a population standard deviation of 3.2. a. Calculate the p-value. What is the conclusion if &Icir
> A consumer group has accused a restaurant of using higher fat content than what is reported on its menu. The group has been asked to conduct a hypothesis test to substantiate its claims. a. Is the manager of the restaurant more concerned about a Type I e
> The screening process for detecting a rare disease is not perfect. Researchers have developed a blood test that is considered fairly reliable. It gives a positive reaction in 98% of the people who have that disease. However, it erroneously gives a positi
> The manager of a large manufacturing firm is considering switching to new and expensive software that promises to reduce its assembly costs. Before purchasing the software, the manager wants to conduct a hypothesis test to determine if the new software d
> A polygraph (lie detector) is an instrument used to determine if an individual is telling the truth. These tests are considered to be 95% reliable. In other words, if an individual lies, there is a 0.95 probability that the test will detect a lie. Let th
> For a continuous random variable X with an upper bound of 4, P (0 ≤ X ≤ 2.5) = 0.54 and P (2.5 ≤ X ≤ 4) = 0.16. Calculate the following probabilities. a. P (X < 0) b. P (X > 2.5) c. P (0 ≤ X ≤ 4)
> The cumulative probabilities for a continuous random variable X are P (X ≤ 10) = 0.42 and P (X ≤ 20) = 0.66. Calculate the following probabilities. a. P (X > 10) b. P (X > 20) c. P (10 < X < 20)
> Consider the following cumulative probability distribution. a. Calculate P (X ≤ 3). b. Calculate P (X = 3). c. Calculate P (2 ≤ X ≤ 4). X 1 2 4 P (X<x) 0.15 0.35 0.52 0.78 0.84 1 LO
> Consider the following discrete probability distribution a. Complete the probability distribution. b. Graphically depict the probability distribution and comment on the symmetry of the distribution. c. What is the probability that the random variable X
> Consider the following discrete probability distribution. / / a. Is this a valid probability distribution? Explain. b. Graphically depict this probability distribution. c. What is the probability that the random variable X is less than 40? d. What is t
> A variety of packaging solutions exist for products that must be kept within a specific temperature range. A cold chain distribution is a temperature-controlled supply chain. An unbroken cold chain is an uninterrupted series of storage and distribution a
> Apple products have become a household name in America, with 51% of all households owning at least one Apple product (CNN, March 19, 2012). a. What is the probability that two in a random sample of four households own an Apple product? b. What is the pr
> 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
> A professor uses a relative scale for grading. She announces that 60% of the students will get at least a B, with 15% getting A’s. Also, 5% will get a D and another 5% will get an F. Assume that no incompletes are given in the course. Let Score be define
> Jane Wormley is a professor of management at a university. She expects to be able to use her grant money to fund up to two students for research assistance. While she realizes that there is a 5% chance that she may not be able to fund any student, there
> Census. The accompanying data file 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
> Data are drawn from a bell-shaped distribution with a mean of 5 and a standard deviation of 2.5. a. Approximately what percentage of the observations are positive? b. Approximately what percentage of the observations are not positive?
> The manager at a water park constructed the following frequency distribution to summarize attendance in July and August. Attendance ……………………………………………………………………………………. Frequency 1,000 up to 1,250 …………………………………………………………………………………………. 5 1,250 up to 1,500 ………
> The following table reports the number of people as well as the number of people living below the poverty level across regions in the U.S. for the year 2013. (All numbers are in 1,000s.) a. Graph and interpret the pie chart that summarizes the proporti
> A data set has a mean of 1,500 and a standard deviation of 100. a. Using Chebyshev’s theorem, what percentage of the observations fall between 1,300 and 1,700? b. Using Chebyshev’s theorem, what percentage of the observations fall between 1,100 and 1,9
> The Statistical Abstract of the United States, 2010 provided the following frequency distribution of the number of people (in 1,000s) who live below the poverty level by region. Region ……………………………………………………………………………… Number of People Northeast …………………………
> According to a recent survey, high school girls average 100 text messages daily (The Boston Globe, April 21, 2010). Assume that the survey was based on a random sample of 36 high school girls. The sample standard deviation is computed as 10 text messages
> The one-year return (in %) for 24 mutual funds is as follows: a. Construct the frequency distribution using classes of −20 up to −10, −10 up to 0, etc. b. Construct the relative frequency, the cumu
> A survey conducted by CBS News asked parents about the professions they would want their children to pursue. Parents’ preferences (in %) are summarized in the following table. Profession ………………………………………………………………………... Parents’ Preference Doctor, banker,
> Patrons at a local restaurant were asked to rate their recent experience at the restaurant with respect to its advertised atmosphere of upbeat, comfortable, and clean. Possible responses included Outstanding, Good, OK, and Horrible. The following table s
> Consider the following returns for two investments, A and B, over the past four years: a. Which investment provides the higher return? b. Which investment provides less risk? c. Given a risk-free rate of 1.2%, calculate the Sharpe ratio for each inve
> Suppose at the beginning of 2012 you decide to invest $1,000 in Vanguard’s European Stock Index mutual fund. The following table shows the returns (in %) for the years 2012– 2015. Year ……………………………………………………………………………… Annual Return 2012 ………………………………………………
> The accompanying data file shows, among other variables, median household income and median house value for the 50 states. a. Compute and discuss the range of household income and house value. b. Compute the sample MAD and the sample standard deviation
> Census. The accompanying table shows a portion of median household income (Income in $) and median house value (House Value in $) for the 50 states in 2010 a. Construct a boxplot for household income and use it to identify outliers, if any, and comment
> The monthly closing stock prices (rounded to the nearest dollar) for Starbucks Corp. and Panera Bread Co. for the first six months of 2016 are reported in the following table. a. Calculate the sample variance and the sample standard deviation for each
> The manager of The Cheesecake Factory in Boston reports that on six randomly selected weekdays, the number of customers served was 120, 130, 100, 205, 185, and 220. She believes that the number of customers served on weekdays follows a normal distributio
> Scores on the final in a statistics class are as follows. Calculate and interpret the 25th, 50th, and 75th percentiles. Calculate the interquartile range. Are there any outliers? Is the distribution symmetric? If not, comment on its skewness. 75 25
> Spain was the winner of the 2010 World Cup, beating the Netherlands by a score of 1–0. The ages of the players from both teams were as follows: Construct a stem-and-leaf diagram for each country. Comment on similarities and difference
> Consider the return data (in percent) for the Value mutual fund in Table 3.1. Table 3.1: a. Calculate and interpret the 25th, 50th, and 75th percentiles. b. Calculate the interquartile range. Are there any outliers? c. Is the distribution symmetri
> Suppose the following high temperatures were recorded for major cities in the contiguous United States for a day in July. Construct and interpret a stem-and-leaf diagram. 84 92 96 91 96 94 93 82 81 76 95 84 90 84 98 94 90 83 78 90 88 96 106 78 92
> A sample of patients arriving at Overbrook Hospital’s emergency room recorded the following body temperature readings over the weekend: Construct and interpret a stem-and-leaf diagram. 100.4 99.6 101.5 99.8 102.1 101.2 102.3 101.2
> Consider the following data set: Construct a stem-and-leaf diagram. Is the distribution symmetric? Explain. -64 -52 -73 -82 -85 -80 -79 -65 -50 -71 -80 -85 -75 -65 -77 -87 -72 -83 -73 -80
> Consider the following data set: Construct a stem-and-leaf diagram. Is the distribution symmetric? Explain. 5.4 4.6 3.5 2.8 2.6 5.5 5.5 2.3 3.2 4.2 4.0 3.0 3.6 4.5 4.7 4.2 3.3 3.2 4.2 3.4
> DJIA_2012. For the first three months of 2012, the stock market put up its best firstquarter performance in over a decade (Money.cnn.com, April 9, 2012). The accompanying table shows a portion of the daily price index for the Dow Jones Industrial Average
> FILE Gas_Prices. The accompanying table shows a portion of the average price (in $) for a gallon of gas for the 50 states during April 2012. State …………………………………………………………………………………………………. Price Alabama ………………………………………………………………………………………………… 4.36 Alaska ………
> The accompanying table shows a portion of median house values (in $) for the 50 states as reported by the U.S. Census Bureau in 2010. State ………………………………………………………………………………………. House Value Alabama ………………………………………………………………………………………….. 117600 Alaska …………………
> A popular weight loss program claims that with its recommended healthy diet regimen, users lose significant weight within a month. In order to estimate the mean weight loss of all customers, a nutritionist takes a sample of 18 dieters and records their w
> The following table lists a portion of the average math SAT scores for each state for the year 2009. State …………………………………………………………………………………………. SAT Alabama ……………………………………………………………………………………… 552 Alaska …………………………………………………………………………………………. 516 ⋮ ……………………………
> The following ogive summarizes the salary (in $1,000,000s) for the 30 highest-paid players in the National Basketball Association (NBA) for the 2012 season (www.nba.com, data retrieved March 2012). a. Approximate the percentage of salaries that were le
> Consider the following five-point summary that was obtained from a data set with 200 observations. a. Interpret Q1 and Q3. b. Calculate the interquartile range. Determine whether any outliers exist. c. Is the distribution symmetric? If not, comment o
> Calculate the 20th, 40th, and 70th percentiles for the following data set -300 -257 -325 -234 -297 -362 -255
> The following ogive summarizes the median household income for the 50 states in the United States (U.S. Census, 2010). a. Approximate the percentage of states with median household income less than $50,000. b. Approximate the percentage of states with
> Calculate the 20th, 50th, and 80th percentiles for the following data set 120 215 187 343 268 196 312
> The manager of a nightclub near a local university recorded the ages of the last 100 guests in the following cumulative frequency distribution. Ages ……………………………………………………………………….. Cumulative Frequency 18 up to 22 ……………………………………………………………………………………………. 45 2
> Fifty cities provided information on vacancy rates (in percent) in local apartments in the following frequency distribution Vacancy Rate (in percent) ……………………………………………………………… Frequency 0 up to 3 …………………………………………………………………………………………………… 5 3 up to 6 …………………
> The following relative frequency distribution summarizes the ages of women who had a child in the last year. Ages …………………………………………………………………………………. Relative Frequency 15 up to 20 ………………………………………………………………………………………………. 0.10 20 up to 25 ……………………………………………………
> AccuWeather.com listed the following high temperatures (in degrees Fahrenheit) for 33 European cities on July 21, 2010. a. Construct the frequency distribution using classes of 60 up to 70, 70 up to 80, etc. b. Construct the relative frequency, the cu
> FILE DOW Characteristics. The accompanying table shows a portion of the 30 companies that comprise the Dow Jones Industrial Average (DJIA). The second column shows the year that the company joined the DJIA (Year). The third column shows each company&acir
> The number of text messages sent by 25 13-year-olds over the past month are as follows a. Construct the frequency distribution using classes of 500 up to 600, 600 up to 700, etc. b. Construct the relative frequency distribution, the cumulative frequen
> Kiplinger’s (August 2007) lists the assets (in billions of $) for the 20 largest stock mutual funds (ranked by size) as follows: a. Construct the frequency distribution using classes of 40 up to 70, 70 up to 100, etc. b. Construct the
> Consider the following five-point summary that was obtained from a data set with 500 observations. a. Interpret Q1 and Q3. b. Calculate the interquartile range. Determine whether any outliers exist. c. Is the distribution symmetric? If not, comment o
> Consider the following relative frequency distribution: Class ……………………………………………………………………… Relative Frequency –20 up to –10 ……………………………………………………………………………….. 0.04 –10 up to 0 …………………………………………………………………………………. 0.28 0 up to 10 …………………………………………………………………………………
> Consider the following frequency distribution: Class ……………………………………………………………………………………. Frequencyy 1,000 up to 1,100 ………………………………………………………………………………… 2 1,100 up to 1,200 ………………………………………………………………………………… 7 1,200 up to 1,300 ………………………………………………………………………………… 3
> Consider the following frequency distribution: Class ………………………………………………………………………………… Frequency 10 up to 20 ……………………………………………………………………………………. 12 20 up to 30 ……………………………………………………………………………………. 15 30 up to 40 ……………………………………………………………………………………. 25 40 up to 50
> Consider the following data set: a. Construct the frequency distribution using classes of −10 up to 0, 0 up to 10, etc. How many of the observations are at least 10 but less than 20? b. Construct the relative frequency distribution an
> Calculate the mean, the variance, and the standard deviation of the following discrete probability distribution. / /
> Calculate the mean, the variance, and the standard deviation of the following discrete probability distribution. 10 15 20 P (X = x) 0.35 0.30 0.20 0.15
> Vanguard’s Precious Metals and Mining fund (Metals) and Fidelity’s Strategic Income fund (Income) were two top-performing mutual funds for the years 2000 through 2009. An analysis of annual return data for these two funds provided important information f
> When reviewing the overall strength of a particular firm, financial analysts typically examine the net profit margin. This statistic is generally calculated as the ratio of a firm’s net profit after taxes (net income) to its revenue, expressed as a perce
> A recent survey of 992 people asked: In which professional sport—football, boxing, hockey, or martial arts—is an athlete most likely to sustain an injury that will affect the athlete after he or she retires? (Vanity Fa
> The following table shows Fortune 500’s rankings of America’s 10 largest corporations for 2010. Next to each corporation is its market capitalization (in $ billions as of March 26, 2010) and its total return (in %) to
> Professor Sanchez has been teaching Principles of Economics for over 25 years. He uses the following scale for grading. a. Depict the above probability distribution graphically. Comment on whether or not the probability distribution is symmetric. b. Co
> A 2010 poll conducted by NBC asked respondents who would win Super Bowl XLV in 2011. The responses by 20,825 people are summarized in the following table. Atlanta Falcons …………………………………………………………………………….… 4,040 New Orleans Saints …………………………………………………………………
> A basketball player is fouled while attempting to make a basket and receives two free throws. The opposing coach believes there is a 55% chance that the player will miss both shots, a 25% chance that he will make one of the shots, and a 20% chance that h
> A financial analyst creates the following probability distribution for the performance of an equity income mutual fund. a. Comment on the optimism or pessimism depicted in the analyst’s estimates. b. Convert the above probability dist
> India is the second most populous country in the world, with a population of over 1 billion people. Although the government has offered various incentives for population control, some argue that the birth rate, especially in rural India, is still too hig
> Identify the possible values of the following random variables. Which of the random variables are discrete? a. The advertised size of a round Domino’s pizza. b. The actual size of a round Domino’s pizza. c. The number of daily visitors to Yosemite Nation
> A random sample is drawn from a population with mean μ = 66 and standard deviation σ = 5.5. a. Comment on the sampling distribution of the sample mean with n = 16 and n = 36. b. Can you use the standard normal distribution to calculate the probability th
> In the previous question, suppose that the management decides to use a chart for the analysis. As noted earlier, 10% of produced items are known to be nonconforming. The firm analyzes a batch of production items for 6 weeks and computes the following per
> A variety of packaging solutions exist for products that must be kept within a specific temperature range. Cold chain distribution is particularly useful in the food and pharmaceutical industries. A packaging company strives to maintain a constant temper
> American workers are increasingly planning to delay retirement (U.S. News & World Report, June 30, 2010). According to a Pew Research Center comprehensive survey, 35% of employed adults of age 62 and older say they have pushed back their retirement date.
> In the previous question regarding walking regimens of the residents of Miami, explain how you can obtain a representative sample based on the following sampling strategies: Data from Problem 51: A seminal study conducted by scientists at the Universit
> A seminal study conducted by scientists at the University of Illinois found evidence of improved memory and reasoning for those who took three vigorous 40-minute walks a week over six months (Newsweek, June 28–July 5, 2010). As an assistant manager worki
> Following customer complaints about the quality of service, Dell stopped routing corporate customers to a technical support call center in Bangalore, India (USA TODAY, November 24, 2003). Suppose Dell’s decision to direct customers to call centers outsid
