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Essentials Of Business Statistics Communicating With Numbers 1st Edition Sanjiv Jaggia, Alison Kelly - Solutions
A family is relocating from St. Louis, Missouri, to California. Due to an increasing inventory of houses in St. Louis, it is taking longer than before to sell a house. The wife is concerned and wants to know when it is optimal to put their house on the market. They ask their Realtor friend for help
U.S. consumers are increasingly viewing debit cards as a convenient substitute for cash and checks. The average amount spent annually on a debit card is $7,790 (Kiplinger’s, August 2007). Assume that this average was based on a sample of 100 consumers and that the population standard deviation is
Suppose a 95% confidence interval for the mean salary of college graduates in a town in Mississippi is given by [$36,080, $43,920]. The population standard deviation used for the analysis is known to be $12,000.a. What is the point estimator of the mean salary of all college graduates in this
A manager is interested in estimating the mean time (in minutes) required to complete a job. His assistant uses a sample of 100 observations to report the confidence interval as [14.355, 17.645]. The population standard deviation is known to be equal to 10 minutes.a. Find the sample mean time used
A study reports that recent college graduates from New Hampshire face the highest average debt of $31,048 (The Boston Globe, May 27, 2012). A researcher from Connecticut wants to determine how recent undergraduates from that state fare. He collects data on debt from 40 recent undergraduates.A
An economist wants to estimate the mean hourly wage of all workers. She collects data on 50 hourly wage earners. A portion of the data is shown in the accompanying table; the complete data set, labeled Hourly_Wage, can be found on the text website. Assume that the population standard deviation is
A safety officer is concerned about speeds on a certain section of the New Jersey Turnpike. He records the speeds of 40 cars on a Saturday afternoon. The accompanying table shows a portion of the results; the complete data set, labeled Highway_Speeds, can be found on the text website. Assume that
Find tα,df from the following information.a. α = 0.025 and df = 12b. α = 0.10 and df = 12c. α = 0.025 and df = 25d. α = 0.10 and df = 25
We use the t distribution for the statistical inference of the population mean when the underlying population standard deviation is not known. Under the assumption that the population is normally distributed, find tα/2,df for the following scenarios.a. A 90% confidence level and a sample of 28
A random sample of 24 observations is used to estimate the population mean. The sample mean and the sample standard deviation are calculated as 104.6 and 28.8, respectively.Assume that the population is normally distributed.a. Construct the 90% confidence interval for the population mean.b.
Consider a normal population with an unknown population standard deviation. A random sample results in = 48.68 and s2 = 33.64.a. Compute the 95% confidence interval for µ if and s2 were obtained from a sample of 16 observations.b. Compute the 95% confidence interval for µ if and s2 were
Let the following sample of 8 observations be drawn from a normal population with unknown mean and standard deviation: 22, 18, 14, 25, 17, 28, 15, 21.a. Calculate the sample mean and the sample standard deviation.b. Construct the 80% confidence interval for the population mean.c. Construct the 90%
A random sample of eight drugstores shows the following prices (in $) of a popular pain reliever:Assume the normal distribution for the underlying population to construct the 90% confidence interval for the population mean.
As reported by tradingeconomics.com on September 2, 2012, the unemployment rates (in %) in major economies around the world are as follows:CountryUnemployment Rate (in %)Australia...........5.2China...........4.1France...........10.0Germany...........6.8India...........3.8United
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 weight loss one month after joining the
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 distribution. Construct the 90% confidence interval for
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 daily.a. Calculate the margin of error with
The Chartered Financial Analyst (CFA®) designation is fast becoming a requirement for serious investment professionals. Although it requires a successful completion of three levels of grueling exams, it also entails promising careers with lucrative salaries. A student of finance is curious about
The Sudoku puzzle has recently become very popular all over the world. It is based on a 9 x 9 grid and the challenge is too ill in the grid so that every row, every column, and every 3 x 3 box contains the digits 1 through 9. A researcher is interested in estimating the average time taken by a
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 companies in the United States. She takes a random
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
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.MonthClosing Stock PriceJanuary 2010.....$71February 2010.....73March 2010.....76April 2010.....78May 2010.....81June 2010.....75a. Calculate
The following table shows the annual returns (in percent) for Fidelity’s Electronic and Utilities funds.a. Derive 99% confidence intervals for the mean return of Fidelity’s Electronic and Utilities funds.b. What did you have to assume to make the aboveinferences?
Suppose the 90% confidence interval for the mean SAT scores of applicants at a business college is given by [1690, 1810]. This confidence interval uses the sample mean and the sample standard deviation based on 25 observations. What are the sample mean and the sample standard deviation used for the
A teacher wants to estimate the mean time (in minutes) students take to go from one classroom to the next. His research assistant uses the sample time of 36 students to report the confidence interval as [8.20, 9.80].a. Find the sample mean time used to compute the confidence interval.b. Determine
In order to lure female customers, a new clothing store offers free gourmet coffee and pastry to its customers. The average daily revenue over the past five-week period has been $1,080 with a standard deviation of $260. Use this sample information to construct the 95% confidence interval for the
Many of today’s leading companies, including Google, Microsoft, and Facebook, are based on technologies developed within universities. Lisa Fisher is a business school professor who believes that a university’s research expenditure in $ millions (Research) and the age of its technology transfer
An associate dean of a university wishes to compare the mean on the standardized final exams in microeconomics and macroeconomics. He has access to a random sample of 40 scores from each of these two courses. A portion of the data is shown below; the complete data set, labeled Economics, can be
For decades, people have believed that boys are innately more capable than girls in math. In other words, due to the intrinsic differences in brains, boys are better suited for doing math than girls. Recent research challenges this stereotype, arguing that gender differences in math performance
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, labeled Debt_Payments, can be found on the text website. Use
A random sample of 100 observations results in 40 successes.a. What is the point estimate for the population proportion of successes?b. Construct the 90% confidence interval for the population proportion.c. Construct the 99% confidence interval for the population proportion.
A random sample of 80 observations results in 50 successes.a. Construct the 95% confidence interval for the population proportion of successes.b. Construct the 95% confidence interval for the population proportion of failures.
Assume =1 0.6 in a sample of size n = 50.a. Construct the 95% confidence interval for 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?
A sample of 80 results in 30 successes.a. Calculate the point estimate for the population proportion of successes.b. Construct 90% and 99% confidence intervals for the population proportion.c. Can we conclude at 90% confidence that the population proportion differs from 0.5?d. Can we conclude at
In a sample of 30 observations the number of successes equals 18.a. Construct the 88% confidence interval for the population proportion of successes.b. Construct the 98% confidence interval for 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 of debts (Vanity Fair, June 2010).a. At 95% confidence, what is the margin of error?b. Construct the 95% confidence interval for the population proportion of
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 the 95% confidence interval for the
An economist reports that 560 out of a sample of 1,200 middle-income American households actively participate in the stock market.a. Construct the 90% confidence interval for the proportion of middle-income Americans who actively participate in the stock market.b. Can we conclude that the
In a CNNMoney.com poll conducted on July 13, 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 the 90% confidence interval for the proportion of Americans who feel
In a recent poll of 760 homeowners in the United States, one in five homeowners reports having a home equity loan that he or she is currently paying of. Using a confidence coefficient of 0.90, derive an interval estimate for the proportion of all homeowners in the United States that hold a home
In an NBC News/Wall Street Journal poll of 1,000 American adults conducted August 5–9, 2010, 44% of respondents approved of the job that Barack Obama was doing in handling the economy.a. Compute the 90% confidence interval for the proportion of Americans who approved of Barack Obama’s handling
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 the 90% confidence interval for the adult obesity rate in the United States.b.
A recent survey asked 5,324 individuals: What’s most important to you when choosing where to live? The responses are shown by the following frequency distribution.ResponseFrequencyGood jobs........1,969Affordable homes.....799Top schools........586Low crime........1,225Things to do........745a.
A survey conducted by CBS News asked 1,026 respondents: “What would you do with an unexpected tax refund?” The responses are summarized in the following table.ResponseFrequencyPay of debts.........482Put it in the bank......308Spend it..........112I never get a refund.....103Other............
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 the
What is the minimum sample size n required to estimate µ with 90% confidence if the desired margin of error is E = 1.2 ? The population standard deviation is estimated as = 3.5. What happens to n if the desired margin of error decreases to E = 0.7?
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 E = 2.6 ? What happens to n if you decide to estimate µ with 95% confidence?
What is the minimum sample size n required to estimate p with 95% confidence if the desired margin of error E = 0.08 ? The population proportion is estimated as = 0.36 from prior studies. What happens to n if the desired margin of error increases to E = 0.12?
In the planning stage, a sample proportion is estimated as = 40/50 = 0.80. Use this information to compute the minimum sample size n required to estimate p with 99% confidence if the desired margin of error E = 0.12 . What happens to n if you decide to estimate p with 90% confidence?
You wish to compute a 95% confidence interval for 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 for the population proportion is available.
An analyst would like to construct 95% confidence intervals for the mean stock returns in two industries. Industry A is a high-risk industry with a known population standard deviation of 20.6%, whereas Industry B is a lower-risk industry with a known population standard deviation of 12.8%.a. What
The manager of a newly opened Target store wants to estimate the average expenditure of his customers. From a preselected sample, the standard deviation was determined to be $18. The manager would like to construct the 95% confidence interval for the mean customer expenditure.a. Find the
A budget airline wants to estimate what proportion of customers would consider paying $12 for in-light wireless access. Given that the airline has no prior knowledge of the proportion, how many customers would it have to sample to ensure a margin of error of no more than 0.05 for a 90% confidence
Newscasters wish to estimate the proportion of registered voters who support the incumbent candidate in the mayoral election. In an earlier poll of 240 registered voters, 110 had supported the incumbent candidate. Find the sample size required to construct a 90% confidence interval if
A survey by the AARP (Money, June 2007) reported that approximately 70% of people in the 50 to 64 age bracket have tried some type of alternative therapy (for instance, acupuncture or the use of nutrition supplements). Assume this survey was based on a sample of 400 people.a. Identify the relevant
A hair salon in Cambridge, Massachusetts, reports that on seven randomly selected weekdays, the number of customers who visited the salon were 40, 30, 28, 22, 36, 16, and 50. It can be assumed that weekday customer visits follow a normal distribution.a. Construct the 90% confidence interval for the
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 the 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 20, 2007). Assume that these data were based on a sample of 225 workers and that the sample standard deviation is 12
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
The SAT is the most widely used test in the undergraduate admissions process. Scores on the math portion of the SAT are believed to be normally distributed and range from 200 to 800. A researcher from the admissions department at the University of New Hampshire is interested in estimating the mean
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 the 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.YearReturn2005......44.602006......19.682007......37.002008...... 242.872009......38.36a. Calculate the point estimate for µ.b. Construct the 95% confidence interval for µ.c. What assumption did you make when
Students who graduated from college in 2010 owed an average of $25,250 in student loans (New York Times, November 2, 2011). An economist wants to determine if average debt has changed. She takes a sample of 40 recent graduates and finds that their average debt was $27,500 with a standard deviation
A Realtor wants to estimate the mean price of houses in Mission Viejo, California. She collects a sample of 36 recent house sales, a portion of which is shown in the accompanying table; the complete data set, labeled MV_Houses, can be found on the text website. Assume that the population standard
Residents of Hawaii have the longest life expectancies, averaging 81.48 years (www.worldlifeexpectancy.com, data retrieved June 4, 2012). A sociologist collects data on the age at death for 50 recently deceased Michigan residents. A portion of the data is shown in the accompanying table; the
The manager of a minor league baseball team wants to estimate the average fastball speed of two pitchers. He clocks 50 fastballs, in miles per hour, for each pitcher. A portion of the data is shown in the accompanying table; the complete data set, labeled Fastballs, can be found on the text
The new manager of a theater would like to offer discounts to increase the number of tickets sold for shows on Monday and Tuesday evenings. She uses a sample of 30 weeks to record the number of tickets sold on these two days. A portion of the data is shown in the accompanying table; the complete
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 24, 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 market-research concern in Framingham, Massachusetts, 12.1% of sole proprietors are engaging in e-commerce (The Wall Street Journal, July 26, 2007).a. With 95% confidence, what is the margin of error when estimating the proportion of sole
A Monster.com poll of 3057 individuals asked: “What’s the longest vacation you plan to take this summer?” The following relative frequency distribution summarizes the results.ResponseRelative FrequencyA few days...............0.21A few long weekends..........0.18One week...............0.36Two
A recent study examined “sidewalk rage” in an attempt to find insight into anger’s origins and offer suggestions for anger-management treatments (The Wall Street Journal, February 15, 2011). “Sidewalk ragers” tend to believe that pedestrians should behave in a certain way. One possible
According to a recent report by the PEW Research Center, 85% of adults under 30 feel optimistic about the economy, but the optimism is shared by only 45% of those who are over 50 (Newsweek , September 13, 2010). A research analyst would like to construct 95% confidence intervals for the proportion
Find the required sample size for estimating the population mean in order to be 95% confident that the sample mean is within 10 units of the population mean. Assume that the population standard deviation is 40.
You need to compute a 99% confidence interval for 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.)
An analyst from an energy research institute in California wishes to precisely estimate the 99% confidence interval for 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
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 inches and 1.8 inches, respectively. She subsequently computes the 95%
Mortgage lenders often use FICO ® scores to check the credit worthiness of consumers applying for real estate loans. In general, FICO scores range from 300 to 850 with higher scores representing a better credit pro. A lender in a mid-western town would like to estimate the mean credit score of its
Subprime lending was big business in the United States in the mid-2000s, when lenders provided mortgages to people with poor credit. However, subsequent increases in interest rates coupled with a drop in home values necessitated many borrowers to default. Suppose a recent report kind that two in
A student of business is interested in estimating the 99% confidence interval for 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
Over a 10-year sample period, the mean return and the standard deviation of annual returns on a portfolio you are analyzing were 10% and 15%, respectively. You assume that returns are normally distributed. Construct the 95% confidence interval for the population mean.
Linda Barnes has learned from prior studies that one out of five applicants gets admitted to top MBA programs in the country. She wishes to construct her own 90% confidence interval for the acceptance rate in top MBA programs. How large a sample should she take if she does not want the acceptance
An economist would like to estimate the 95% confidence interval for the average real estate taxes collected by a small town in California, ravaged by the economic crisis. In a prior analysis, the standard deviation of real estate taxes was reported as $1,580. What is the minimum sample size
An employee of the Bureau of Transportation Statistics has been given the task of estimating the proportion of on-time arrivals of a budget airline. A prior study had estimated this on-time arrival rate as 78.5 percent. What is the minimum number of arrivals this employee must include in the sample
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 the 95% confidence interval of the
There is a declining interest among teenagers to pursue a career in science and health care (US News and World Report, May 23, 2011). Thirty college-bound students in Portland, Oregon, are asked about the field they would like to pursue in college. The choices offered in the questionnaire are
Texas is home to more than one million undocumented immigrants and most of them are stuck in low-paying jobs. Meanwhile, the state also suffers from a lack of skilled workers. The Texas Workforce Commission estimates that 133,000 jobs are currently unfilled, many because employers cannot find
The following table presents the returns of two mutual funds offered by the investment giant Fidelity. The Fidelity Select Automotive Fund invests primarily in companies engaged in the manufacturing, marketing, or sales of automobiles, trucks, specialty vehicles, parts, tires, and related
The information gathered from opinion polls and political surveys is becoming so increasingly important for candidates on the campaign trail that it is hard to imagine an election that lacks extensive polling. An NBC News/ Wall Street Journal survey (August 5–9, 2010) of 1,000 adults
Explain why the following hypotheses are not constructed correctly.a. H0: ≤ 10; HA: ≥ 10b. H0: ≠ 500; HA: µ = 500c. H0 : p ≤ 0.40; HA: p > 0.42d. H0 : ≤ 128; HA: > 128
Which of the following statements are valid null and alternative hypotheses? If they are invalid hypotheses, explain why.a. H0 : ≤ 210; HA: > 210b. H0: µ = 120; HA: µ ≠ 120c. H0: p ≤ 0.24; HA: p > 0.24d. H0: < 252; HA: µ > 252
Explain why the following statements are not correct.a. “With my methodological approach, I can reduce the Type I error with the given sample information without changing the Type II error.”b. “I have already decided how much of the Type I error I am going to allow. A bigger sample will not
Which of the following statements are correct? Explain if incorrect.a. “I accept the null hypothesis since sample evidence is not inconsistent with the null hypothesis.”b. “Since sample evidence cannot be supported by the null hypothesis, I reject the null hypothesis.”c. “I can establish
Define the consequences of Type I and Type II errors for each of the tests considered in the preceding question.
Discuss the consequences of Type I and Type II errors for each of the claims considered in the preceding question.
A polygraph (lie detector) is an instrument used to determine if the 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 there also be a 0.005 probability that the
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 positive reaction in 3% of the people who do not
The manager of a large manufacturing firm is considering switching to new and expensive software that promises to significantly reduce its assembly costs. Before purchasing the software, the manager wants to conduct a hypothesis test to determine if the new software does significantly reduce its
A consumer group has accused a restaurant for 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 Type I or Type II error? Explain.b. Is the consumer
Consider the following hypotheses:H0: µ ≤ 12.6HA: µ > 12.6A sample of 25 observations yields a sample mean of 13.4. Assume that the sample is drawn from a normal population with a known population standard deviation of 3.2.a. Calculate the p-value.b. What is the conclusion if α = 0.10?c.
Redo the preceding question using the critical value approach.
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