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business statistics communicating
Business Statistics Communicating With Numbers 1st Edition Kelly Jaggia - Solutions
FILE (Use Excel) The SAT is required of most students applying for college admission in the United States. This standardized test has gone through many revisions over the years. In 2005, a new writing section was introduced that includes a direct writing measure in the form of an essay. People
A random sample of 25 observations is used to estimate the population variance. The sample mean and sample standard deviation are calculated as 52.5 and 3.8, respectively. Assume that the population is normally distributed. P-399a. Construct a 90% interval estimate of the population variance.b.
In order to derive a confidence interval of the population variance, a random sample of n observations is drawn from a normal population. Use this information to find χ2α/2,df and χ21 − α/2,df under the following scenarios. P-399a. A 95% confidence level with n = 18.b. A 95% confidence level
Conduct a hypothesis test for the ratio of two population variances.P-399
Construct a confidence interval for the ratio of two population variances. P-399
Discuss features of the F distribution. P-399
Conduct a hypothesis test for the population variance. P-399
Construct a confidence interval for the population variance. P-399
Discuss features of the x distribution. P-399
F IL E (Use Excel) The accompanying table shows annual return data from 2001– 2009 for Vanguard's Balanced Index and European Stock Index mutual funds. The data can also be accessed from the text website, labeled Vanguard Balanced and European Funds. PG-69a. Set up the hypotheses to test w hether
A new study has found that, on average, 6- to 12-year-old children are spending less time on 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 two
FILE (Use Excel) The following table shows the annual returns (in percent) for Fidelity's Select Electronic and Select Utilities mutual funds. These data can also be found on the text website, labeled Electronic and Utilities. PG-69a. Set up the hypotheses to test the claim that the mean return for
The nutritionist from Exam ple 10,7 also w ants to use the data from the 4 0 Starbucks cardholders in order to determ ine if the posting o f caloric inform ation has reduced the intake of average food calories. This test is also conducted at the 5% significance level. PG-69
Despite his inexperience and some perception that he is a risky choice, candidate A appears to have gained support among the electorate. Three months ago, in a survey of 120 registered voters, 55 said that they would vote for Candidate A. Today, 41 registered voters in a sample of 80 said that they
Let’s revisit Example 10.9. Specify the competing hypotheses in order to determine whether the proportion of those who favor Candidate A has changed over the threemonth period. Using the 95% confidence interval, what is the conclusion to the test?Explain. PG-69
Recent research by analysts and retailers claims significant gender differences when it comes to online shopping (The Wall Street Journal, March 13, 2008).A survey revealed that 5,400 of 6,000 men said they “regularly” or “occasionally” make purchases online, compared with 8,600 of 10,000
While we expect relatively expensive wines to have more desirable characteristics than relatively inexpensive wines, people are often confused in their assessment of the quality of wine in a blind test (New York Times, December 16, 2010).In a recent experiment at a local winery, the same wine is
FILE(Use Excel) An engineer wants to determine the effectiveness of a safety program. He collects annual loss of hours due to accidents in 12 plants "before and after" the program was put into operation. The data can be found on the text website, labeled Safety Program.Plant Before After Plant
A recent Health o f Boston report suggests that 14% o f female residents suffer from asthma as opposed to 6% of males (The Boston Globe, August 16, 2010). Suppose 250 females and 200 males responded to the study.a. Develop the appropriate null and alternative hypotheses to test whether the
According to th e Pew report, 14.6% o f new ly married c o u p l e s in 2 0 0 8 r ep o rted th a t their s p o u s e w a s o f a n o t h e r race or ethnicity (CNNLiving, J u n e 7 , 2 0 1 0 ). In a sim ilar su r v ey in 19 8 0 , o n ly 6.8% o f n e w l y w e d c o u p l e s r ep o rted m arrying o
A recent study claims that girls and boys do not do equally well on math tests taken from the 2nd to 11th grades (The Chicago Tribune, July 2 5 , 2008). Suppose in a representative sample, 344 of 430 girls and 369 of 450 boys score at proficient or advanced levels on a standardized math test.a.
Given construct a 90% con fid en ce interval for th e difference b e tw e e n t h e p o p u la tio n p r o p o rtio n s. Is th e r e a statistical d iffe re n ce b e tw e e n th e population proportions at th e 10% significance level? Explain. PG-69
Given x 1 = 50, n 1 = 2 0 0 , x 2 = 70, n 2 = 2 5 0 construct a 95%c o n f id e n c e interval for t h e d ifference b e t w e e n t h e p o p u la tio n p roportion s. Is t h e r e a statistical d ifferen ce b e t w e e n t h e population proportions at th e 5% significance level? Explain. PG-69
ES(Use Excel) A recent report criticizes SAT-testpreparation providers for promising big score gains without any hard data to back up such claims (The Wall Street Journal, May 2 0 , 2009). Suppose eight college-bound students take a mock SAT, complete a three-month test-prep course, and then take
FILE (Use Excel) Researchers at The Wharton School of Business have found that men and wom en shop for different reasons (Knowledge@Wharton, November 2 8 , 2007). 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,
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 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. PG-69a.
Consider the following matched samples representing observations before and after an experiment. Assume that sample data are drawn from two normally distributed populations.a. Construct the competing hypotheses to determine if the experiment increases the magnitude of the observations.b. Implement
A sample of 35 paired observations generates the following results: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 conclude that the mean
Consider th e follow ing c o m p e tin g h y p o th eses and accom panying sam ple results.Hypotheses: H0: μD ≤ 0; H A: μD > 2 Sam ple results:a. Calculate t h e v a lu e o f t h e t e s t statistic. A s s u m e n o rm ality to approxim ate the p -value.b. U se t h e 1 % s ig n ific a n c e
C onsider t h e f o llo w in g c o m p e t in g h y p o t h e s e s a n d accom panying sam ple results. PG-69 Hypotheses: H0: μD ≥ 0; HA: μD < 0 Sam ple results:a. C alculate t h e v a lu e o f t h e t e s t statistic u n d e r t h e a ssu m p tio n th at th e difference is normally
The following table contains information on matched samples drawn from populations that are assumed to be normally distributed. PG-69a. C onstruct a 95% c o n f id e n c e interval for t h e m e a n difference μ D .b. Specify th e c o m p e tin g h y p o th e se s in order to test w h eth er th e
A s a m p le o f 2 0 p a ired o b s e r v a tio n s g e n e r a t e s t h e f o llo w in g data: A s s u m e 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. PG-69
(Use Excel) Baseball has always been a favorite pastime in America, and is rife w ith statistics and theories. While baseball purists may disagree, to an applied statistician no topic in baseball is too small or hypothesis too unlikely. In a recent paper, researchers at Wayne State University
(Use Excel) According to a study published in the New England Journal o f Medicine, overweight people on lowcarbohydrate and Mediterranean diets lost more weight and got greater cardiovascular benefits than people on a conventional low-fat diet (The Boston Globe, July 17, 2008).A nutritionist
(Use Excel) A consumer advocate researches the length of life between two brands of refrigerators, Brand A and Brand B. He collects data on the longevity of 40 refrigerators for Brand A and repeats the sampling for Brand B. These data are measured in years and can be found on the text website,
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
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
Consider the following sample data drawn independently from normally distributed populations with unequal population variances. PG-69a. Construct the relevant hypothesis to test if the means of the two populations differ.b. What is the value of the test statistic?c. Approximate the p-value of the
Consider the following sample data drawn independently from normally distributed populations with equal population variances. PG-69a. Construct the relevant hypotheses to test if the mean of the second population is greater than the mean of the first population.b. What is the inference of the test
Consider the following competing hypotheses and accompanying sample data. PG-69Assume that the populations are normally distributed with unknown but equal variances.a. Calculate the value of the test statistic.b. Using the p-value approach, test the above hypotheses at the 5% significance level.c.
Consider the following competing hypotheses and accompanying sample data drawn independently from normally distributed populations. PG-69a. Implement the test at the 5% level under the assumption that the population variances are unknown but equal.b. Implement the test at the 5% level under the
Consider the following competing hypotheses and accompanying sample data. The two populations are known to be normally distributed. PG-69a. Implement the test at the 5% level under the assumption that the population variances are unknown but equal.b. Repeat the analysis at the 10% level. H-0 H->0 X
Consider the following data: PG-69a. Construct a 95% confidence interval for the difference between the population means.b. Specify the competing hypotheses in order to determine whether or not the population means differ.c. Using the confidence interval from parta, can you reject the null
Make inferences about the difference between two population proportions based on independent sampling. PG-69
Make inferences about the mean difference based on matched-pairs sampling. PG-69
Make inferences about the difference between two population means based on independent sampling. PG-69
W hat is the probability that a reader carries at least two credit c? L05
You have a choice of receiving $ 1,000 in cash or receiving a beautiful painting from your grandmother. The actual value of the painting is uncertain. You are told that the painting has a 20% chance of being worth $2,000, a 50% chance of being worth$1,000, and a 30% chance of being worth $500. W
Using the information in Example 5.5, answer the following questions.a. Calculate and interpret the correlation coefficient between the returns on Stocks A and B.b. Calculate the portfolio variance using both formulas.c. Calculate the portfolio standard deviation.d. Comment on the findings. L05
From past experience, a manager of an upscale shoe store knows that 85% of her customers will use a credit card when making purchases. Suppose three customers are in line to make a purchase.a. Does this example satisfy the conditions of a Bernoulli process?b. Construct a probability tree that
Approximately 20% of U.S. workers are afraid that they will never be able to retire(bankrate.com, June 23, 2008). Suppose 10 workers are randomly selected.a. W hat is the probability that none of the workers is afraid that they will never be able to retire?b. W hat is the probability that at least
In 2007 approximately 4.7% of the households in the Detroit metropolitan area were in some stage of foreclosure, the highest foreclosure rate in the nation (The Associated Press, February 13, 2008). Suppose we sample 100 mortgage-holding households in the Detroit area.a. W hat is the probability
We can now address questions first posed by Anne Jones in the introductory case of this chapter. Recall that Anne is concerned about staffing needs at the Starbucks that she manages. She has specific questions about the probability distribution of customer arrivals at her store. Anne believes that
Last year, even as a recession gripped the country, 114 microbreweries and brewpubs opened in the United States (The Wall Street Journal, March 18, 2009). Assume this number represents an average and remains constant over time. Solve the following probabilities with Excel.a. What is the probability
Wooden boxes are commonly used for the packaging and transportation of mangoes. A convenience store in Morganville, New Jersey, regularly buys mangoes from a wholesale dealer. For every shipment, the manager randomly inspects five mangoes from a box containing 20 mangoes for damages due to
(Use com puter) Many U.S. households still do no t have In ternet access. Suppose 20 ou t of 80 households in a small so uthern tow n do no t have In ternet access. A com pany th a t provides high sp eed Internet has recently en tered th e m arket. As part of th e m arketing cam paign, th e com
A professor has learned th a t th ree stu d en ts in her class of 20 will ch eat on th e exam . She decides to focus her atten tio n on four random ly chosen stu d e n ts during th e exam .a. W hat is th e probability th a t sh e finds at least o n e of th e stu d e n ts cheating?b. W hat is th e
(Use computer) Despite the fact that hom e prices seem affordable and m ortgage rates are at historic lows, real estate agents say they are showing more homes, but not selling more (The Boston Globe, March 7 , 2009). A real estate company estim ates that an average of five people show up at an open
Studies have shown that bats can consume an average of 10 mosquitoes per minute (berkshiremuseum.org).a. Calculate the average number of mosquitoes that a bat consumes in a 30-second interval.b. W hat is th e probability th a t a bat consum es 4 m osquitoes in a 30-second interval?c. W hat is th e
(Use computer) According to a survey by consulting firm Watson Wyatt, approximately 19% of employers have eliminated perks or plan to do so in the next year (Kiplinger's Personal Finance, February 2009). Suppose 30 employers are randomly selected.a. What is the probability that exactly 10 of the
(Use computer) Twenty percent of U.S. mortgages are"underwater" (The Boston Globe, March 5 , 2009). A mortgage is considered underwater if the value of the home is less than what is owed on the mortgage. Suppose 100 mortgage holders are randomly selected.a. What is the probability that exactly 15
According to the Department o f Transportation, 27% of domestic flights were delayed last year (Money, May 2008). At New York's John F. Kennedy Airport, five flights are randomly selected.a. What is the probability that all five flights are delayed?b. What is the probability that all five are on
Forty-four percent of consumers with credit cards carry balances from month to month (bankrate.com, February 20, 2007). Four consumers with credit cards are randomly selected.a. What is the probability that all consumers carry a credit card balance?b. What is the probability that fewer than two
Facing the worst economic climate since the dot-com bust in the early 2000s, high-tech companies in the U.S. search for investment opportunities with cautious optimism (USA Today, February 17, 2009). Suppose the investment team at Microsoft is considering an innovative start-up project.According to
(Use computer) Powerball is a jackpot game with a grand prize starting at $20 million and often rolling over into the hundreds of millions. In 2006, the jackpot was $365 million.The winner may choose to receive the jackpot prize paid over 29 years or as a lump sum payment. For $1 the player selects
(Use computer) A committee of 40 members consists of 24 men and 16 women. A subcommittee consisting of 10 randomly selected members will be formed.a. What are the expected number of men and women in the subcommittee?b. What is the probability that at least half of the members in the subcommittee
The National Science Foundation is fielding applications for grants to study climate change. Twenty universities apply for a grant, and only 4 of them will be awarded. If Syracuse University and Auburn University are among the 20 applicants, what is the probability that these two universities will
David Barnes and his fiancee Valerie Shah are visiting Hawaii. There are 20 guests registered for orientation. It is announced that 12 randomly selected registered guests will receive a free lesson of the Tahitian dance.a. What is the probability that both David and Valerie get picked for the
Many programming teams work independently at a large software company. The management has been putting pressure on these teams to finish a project on time. The company currently has 18 large programming projects, of which only 12 are likely to finish on time. Suppose the manager decides to randomly
Despite the repeated effort by the government to reform how Wall Street pays its executives, some of the nation's biggest banks are continuing to pay out bonuses nearly as large as those in the best years before the crisis (The Washington Post, January 15, 2010). It is known that 10 out of 15
(Use computer) Compute the probability o f at least 8 successes in a random sample o f 20 items obtained from a population of 100 items that contains 25 successes. What are the expected number and the standard deviation of successes? L05
(Use computer) Assume that X is a hypergeometric random variable with N = 50, 5 = 20, and n = 5. Calculate the following probabilities. L05a. P(X = 2)b. P(X ≥ 2)c. P(X ≤ 3)
Compute the probability of no success in a random sample of 3 items obtained from a population of 12 items that contains 2 successes. What are the expected number and the standard deviation of successes from the sample? L05
Assume that X is a hypergeometric random variable with N = 15, S = 4, and n = 3. Calculate the following probabilities. L05a. P(X = 1)b. P(X = 2)c. P(X ≥ 2)
Assume that X is a hypergeometric random variable with N = 25, 5 = 3, and n = 4. Calculate the following probabilities. L05a. P(X = 0)b. P(X = 1)c. P(X ≤ 1)
(Use computer) In the fiscal year that ended September 30, 2008, there were 24,584 age-discrimination claims filed with the Equal Employment Opportunity Commission, an increase of 29% from the previous year (The Wall Street Journal, March 7– 8,2009). Assume there were 260 working days in the
(Use computer) On average, 400 people a year are struck by lightning in the United States (The Boston Globe, July 21, 2008).a. What is the probability that at most 425 people are struck by lightning in a year?b. What is the probability that at least 375 people are struck by lightning in a year? L05
According to a recent government report, the aging of the U.S. population is translating into many more visits to doctors' offices and hospitals (USA Today, August 7 , 2008). It is estimated that an average person makes four visits a year to doctors' offices and hospitals.a. What is the mean and
Motorists arrive at a Gulf gas station at the rate of two per minute during morning hours.a. What is the probability that more than two motorists will arrive at the Gulf gas station during a one-minute interval in the morning?b. What is the probability that exactly six motorists will arrive at the
Airline travelers should be ready to be more flexible as airlines once again cancel thousands of flights this summer.The Coalition for Airline Passengers Rights, Health, and Safety averages 400 calls a day to help stranded travelers deal with airlines (seattlepi.com, July 10, 2008). Suppose the
A tollbooth operator has observed that cars arrive randomly at an average rate of 360 cars per hour.a. Find the probability that 2 cars arrive during a specified 1-minute period.b. Find the probability that at least 2 cars arrive during a specified 1-minute period.c. Find the probability that 40
A textile manufacturing process finds that on average, two flaws occur per every 50 yards of material produced.a. What is the probability of exactly 2 flaws in a 50-yard piece of material?b. What is the probability of no more than two flaws in a 50-yard piece of material?c. What is the probability
(Use computer) Assume th a t X is a Poisson random variable with μ = 20. Calculate the following probabilities.a. P(X < 14)b. P(X ≥ 20)c. P(X = 25)d. P(18 ≤ X ≤ 23) L05
(Use computer) Assume that X is a Poisson random variable w ith μ = 15. Calculate the following probabilities. L05a. P(X ≤ 10)b. P(X = 13)c. P(X > 15)d. P(12 ≤ X ≤ 18)
Let the mean success rate of a Poisson process be 8 successes per hour.a. Find the expected number of successes in a half-hour period.b. Find the probability of at least 2 successes in a given half-hour period.c. Find the expected number of successes in a two-hour period.d. Find the probability of
Assume that X is a Poisson random variable w ith μ = 4.Calculate the following probabilities. L05a. P(X = 4)b. P(X= 2)c. P(X ≤ 1)
Assume that X is a Poisson random variable with μ = 1.5.Calculate the following probabilities. L05a. P(X = 1)b. P(X = 2)c. P( X ≥ 2)
(Use computer) The Washington, D.C., region has one of the fastest-growing foreclosure rates in the nation, as 15,613 homes went into foreclosure during the one-year period ending in February 2008 (The Washington Post, June 19,2008). Over the past year, the number of foreclosures per 10,000 is 131
(Use computer) At the University of Notre Dame Mendoza College of Business, 40% of the students seeking a master's degree specialize in finance (Kiplinger's Personal Finance, March 2009). Twenty master's degree students are randomly selected.a. What is the probability that exactly 10 of the
(Use computer) Suppose 40% of recent college graduates plan on pursuing a graduate degree. Fifteen recent college graduates are randomly selected.a. What is the probability that no more than four of the college graduates plan to pursue a graduate degree?b. What is the probability that exactly seven
According to the U.S. Census, roughly half of all marriages in the United States end in divorce. Researchers from leading universities have shown that the emotions aroused by one person's divorce can transfer like a virus, making divorce contagious (CNN, June 10, 2010). A splitup between immediate
Sikhism, a religion founded in the 15th century in India, is going through turmoil due to a rapid decline in the number o f Sikh youths w ho wear turbans (Washington Post, March 29, 2009). The tedious task of combing and tying up long hair and a desire to assimilate has led to approximately 25% of
Approximately 76% of baby boomers aged 43 to 6 1 are still in the workforce (The Boston Globe, July 10, 2008). Six baby boomers are selected at random.a. What is the probability that exactly one of the baby boomers is still in the workforce?b. What is the probability that at least five of the baby
In recent analyses of Census figures, one in four American counties have passed or are approaching the tipping point where black, Hispanic, and Asian children constitute a majority of the under-20 population (New York Times, August 6 , 2008). Racial and ethnic minorities now account for 43% of
The percentage of Americans who have confidence in U.S.banks dropped to 23% in June 2010, which is far below the pre-recession level of 41% reported in June 2007(gallup.com).a. What is the probability that fewer than half of 10 Americans in 2010 have confidence in U.S. banks?b. What would have been
At a local commuter college, 40% of students who enter the college as freshmen go on to graduate. Ten freshmen are randomly selected.a. What is the probability that none of them graduates from the local university?b. What is the probability that at most nine will graduate from the local
According to a report from the Center for Studying Health System Change, 20% of Americans delay or go without medical care because of concerns about cost (The Wall Street Journal, June 26, 2008). Suppose eight individuals are randomly selected.a. What is the probability that none will delay or go w
(Use computer) Let X represent a binomial random variable with n = 200 and p = 0.77. Find the following probabilities. L05a. P(X ≤ 150)b. p(X > 160)c. P(155 ≤ X ≤ 165)d. P(X = 160)
(Use computer) Let X represent a binomial random variable with n = 150 and p = 0.36. Find the following probabilities. L05a. P(X ≤ 50)b. P(X = 40)c. P(X > 60)d. P(X ≥ 55)
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