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business statistics communicating

Business Statistics Communicating With Numbers 1st Edition Kelly Jaggia - Solutions

Conduct and evaluate hypothesis tests based on two-way ANOVA with no interaction. P-69
Use confidence intervals and Tukey's HSD method in order to determine which means differ. P-69
Conduct and evaluate hypothesis tests based on one-way ANOVA. P-69
Provide a conceptual overview of ANOVA. P-69
A trade group predicts that back-to-school spending will average $606.40 per family this year. A different economic model is needed if the prediction is wrong. Specify the null and the alternative hypotheses to determine if a different economic model may be needed. P-56
Consider the following hypotheses that relate to the medical example mentioned earlier.H0: A person is free of disease HA: A person has disease Suppose a person takes a medical test that attempts to detect the disease. Discuss the consequences of a Type I error and a Type II error. P-56
A research analyst disputes a trade group’s prediction that back-to-school spending will average $606.40 per family this year. She believes that average back-to-school spending will significantly differ from this amount. She decides to conduct a test on the basis of a random sample of 30
Repeat Example 9.7 using the critical value approach. Recall that a research analyst wishes to determine if average back-to-school spending differs from $606.40.A random sample of 30 households, drawn from a normally distributed population with a standard deviation of $65, results in a sample mean
In the introductory case to this chapter, the dean at a large university in California wonders if students at her university study less than the 1961 national average of 24 hours per week. She randomly selects 35 students and asks their average study time per week (in hours). From their responses
As the introductory case to this chapter mentions, recent research finds that today’s undergraduates study an average of 14 hours per week. Using the sample data from Table 9.1, the dean would also like to test if the mean study time of students at her university differs from today’s national
A popular weekly magazine asserts that fewer than 40% of households in the United States have changed their lifestyles because of escalating gas prices. A recent survey of 180 households finds that 67 households have made lifestyle changes due to escalating gas prices.a. Specify the competing
Since the statistical conclusion of a hypothesis test relies on sample data, there are two types of errors that may occur: a Type I error or a Type II error. A Type I error is committed when we reject the null hypothesis when it is actually true. On the other hand, a Type II error is made when we
A Pew Research study finds that 23% of Americans use only a cell phone, and no land line, for making phone calls (The Wall Street Journal, October 14, 2010). A year later, a researcher samples 200 Americans and finds that 51 of them use only cell phones for making phone calls.a. Set up the
A television network is deciding whether or not to give its newest television show a spot during prime viewing time at night. For this to happen, it will have to move one of its most viewed shows to another slot. The network conducts a survey asking its viewers which show they would rather
The lingering economic crisis has cost America trillions of dollars in lost wealth and also has levied a heavy toll on the national psyche (The Wall Street Journal, December 21, 2009).According to a recent poll, just 33% of those surveyed said America was headed in the right direction. Suppose this
A retailer is looking to evaluate its customer service.Management has determined that if the retailer wants to stay competitive, then it will have to have at least a 90%satisfaction rate among its customers. Management will take corrective actions if the satisfaction rate falls below 90%. A survey
(Use Excel) An entrepreneur examines monthly sales(in $ 1,000s) for 40 convenience stores in Rhode Island.Access the convenience store sales data on the text website(Convenience Stores).a. State the null and the alternative hypotheses in order to test whether average sales differ from $130,000.b.
(Use Excel) An investor wants to test whether the average return of Vanguard's Precious Metals and Mining Fund is greater than 12% based on data over the past 25 years. Assume returns are normally distributed with a population standard deviation of 30%.a. State the null and the alternative
Rates on 30-year fixed mortgages continue to be at historic lows (Chron Business News, September 23, 2010). According to Freddie Mac, the average rate for 30-year fixed loans for the week was 4.37%. An economist wants to test if there is any change in the mortgage rates in the following week.She
A city council is deciding whether or not to spend additional money to reduce the amount of traffic. The council decides that it will increase the transportation budget if the amount of waiting time for drivers exceeds 20 minutes. A sample of 32 main roads results in a mean waiting time of 22.08
An advertisement for a popular weight loss clinic suggests that participants in its new diet program lose, on average, more than 10 pounds. A consumer activist decides to test the authenticity of the claim. She follows the progress of 18 women who recently joined the weight reduction program.She
A phone manufacturer wants to compete in the touch screen phone market. He understands that the lead product has a battery life of just 5 hours. The manufacturer claims that while the new touch phone is more expensive, its battery life is more than twice as long as that of the leading product. In
The Social Security Administration is not expected to provide any increases in Social Security benefits for the second straight year (US News & World Report, October 4 , 2010).With increasing medical prices, it is claimed that more than 60% of seniors are likely to make serious adjustments to their
New research shows that many banks are unwittingly training their online customers to take risks with their passwords and other sensitive account information, leaving them more vulnerable to fraud (Yahoo.com, July 23, 2008). Even websavvy surfers could find themselves the victims of identity theft
A movie production company is releasing a movie with the hopes of many viewers returning to see the movie in the theater for a second time. Their target is to have 30 million viewers, and they want more than 30% of the viewers to return to see the movie again. They show the movie to a test audience
The margarita is one of the most common tequila-based cocktails, made with tequila mixed with triple sec and lime or lemon juice, often served with salt on the glass rim.A common ratio for a margarita is 2:1:1, which includes 50% tequila, 25% Triple Sec, and 25% fresh lime or lemon juice. A manager
Due to the recent economic downturn, Americans have started raiding their already fragile retirement accounts to endure financial hardships such as unemployment, medical emergencies, and buying a home (MSN Money, July 16, 2008). It is reported that between 1998 and 2004, about 12% of families with
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). In October 2010, Massachusetts enacted a law that forbids cell phone use by drivers under the age o f 18. A policy analyst w ould like to determ ine w
(Use Excel) A recent study found that consumers are m aking average m onthly debt payments o f $983 (Experian.com, Novem ber 1 1 , 2010). The accompanying table shows a portion o f average debt payments for 26 m etropolitan areas.The complete data set is on the text website and is labeled Debt
(Use Excel) Access the miles per gallon (MPG) data on the text website labeled MPG.a. State the null and the alternative hypotheses in order to test whether the average MPG differs from 95.b. Use Excel to calculate descriptive statistics for the data, then use the function T.DIST.2T to calculate
A car manufacturer is trying to develop a new sports car.Engineers are hoping that the average amount of time that the car takes to go from 0 to 60 miles per hour is below 6 seconds. The car company tested 12 of the cars and clocked their performance times. Three of the cars clocked in at 5.8
Based on the average predictions of 47 members of the National Association of Business 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 a 5%significance
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 deviation of the bottles are 11.80 ounces and
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 five minutes. She randomly observes the wait
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 weight and standard deviation are calculated as 1.22 pounds and 0.06 pound, respectively.a. Set up the null and the alternative hypotheses to determine if the
Consider the following hypotheses:H0: μ ≥ 100 HA: μ < 100 The population is normally distributed. A sample produces the following observations:95 99 85 80 98 97 Use the critical value approach to conduct the test at a 1 %level of significance.Applications? P-69
Consider the following hypotheses:H0: μ = 8 HA: μ ≠ 8 The population is normally distributed. A sample produces the following observations:6 9 8 7 7 11 10 Use the p-value approach to conduct the test at a 5% level of significance. P-69
Consider the following hypotheses:H0: μ = 12 HA: μ. ≠ 12 Approximate the p-value for this test based on the following sample information.a.b.c.d.critical value approach to implement the test at a 1 % level of significance. P-69
Which of the sample information in the preceding question enables us to reject the null hypothesis at α = 0.01 and atα = 0.10? P-69
In order to test if the population mean differs from 16, you draw a random sample of 32 observations and compute the sample mean and the sample standard deviation as 15.2 and 0.6, respectively. Use (a) the p-value approach and (b) the? P-69 a.b.c.d.
Use the critical value approach to conduct the same two tests in the preceding question at α = 0.05. P-69
In order to conduct a hypothesis test of the population mean, a random sample of 24 observations is drawn from a normally distributed population. The resulting mean and the standard deviation are calculated as 4.8 and 0.8, respectively.Use the p-value approach to conduct the following tests atα =
(Use Excel) Access the weekly stock prices for Home Depot in the data file on the text website (H om e D ep o t).Assume that returns are normally distributed with a population standard deviation of $3.a. State the null and the alternative hypotheses in order to test whether or not the average
(Use Excel) Access the hourly wage data on the text website (Hourly W age). An economist wants to test if the average hourly wage is less than $22.a. State the null and the alternative hypotheses for the test.b. Use the function Z.TEST to calculate the p -value. Assume that the population standard
(Use Excel) A realtor in Mission Viejo, California, believes that the average price of a house is more than $500 thousand.a. State the null and the alternative hypotheses for the test.b. Open the Mission Viejo (raw ) data from the text website into an Excel spreadsheet (data are in $1,000s). Use
In May 2008 CNN reported that Sports Utility Vehicles(SUVs) are plunging toward the "endangered" list. Due to soaring oil prices and environmental concerns, consumers are replacing gas-guzzling vehicles with fuel-efficient smaller cars. As a result, there has been a big drop in the demand for new
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 at 65 miles per hour and records the braking
Customers at Costco spend an average of $130 per trip (The Wal Street Journal, October 6 , 2010). One of Costco's rivals would like to determine whether its customers spend more per trip. A survey of the receipts of 25 customers found that the sample mean was $135.25. Assume that the population
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 test
Construct the null and alternative hypotheses for the following claims:a. "I am going to get the majority of the votes to win this election."b. "I suspect that your 10-inch pizzas are, on average, less than 10 inches in size."c. "I will have to fine the company since its tablets do not contain an
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 change
Which of the following statements are valid null and alternative hypotheses? If they are invalid hypotheses, explain why.b. H0: µ = 120; HA: µ ≠ 120c. H0: p ≤ 0.24; HA: p > 0.24d. H0: µ < 252; HA. µ > 252
Explain why the following hypotheses are not constructed correctly.a. H0: µ ≤ 10; µ≥10b. H0: µ ≠ 500; HA: µ = 500c. H0: p ≤ 0.40; HA: p > 0.42
Specify the test statistic for the population proportion.
Differentiate between the test statistics for the population mean.
Explain the steps of a hypothesis test using the critical value approach.
Explain the steps of a hypothesis test using the p-value approach.
Distinguish between Type I and Type II errors.
Define the null hypothesis and the alternative hypothesis.
FILE (Use Excel) A ccess th e m iles per gallon (m pg) data on th e text w e b site labeled MPG.a. State th e null and th e alternative h y p o th e se s in order to test w h e th e r or n o t th e variance o f m p g differs from 62 m p g 2.b. Calculate th e relevant te st statistic.c. U se Excel's
FILE (U se Excel) A realtor in M ission Viejo, California, b eliev es that th e standard deviation o f h o u se prices is m ore than 100 units, w here each unit equals $1,000. A ssum e hou se prices are normally distributed.a. Sta te t h e null a n d t h e a lternative h y p o t h e s e s for t h e
Rebecca Johnson’s client from the introductory case also wonders if the standard deviation of returns for the Income fund differs from 8.5%. This is equivalent to testing whether or not the variance differs from 72.25(%)2. Use the p-value approach to conduct this test at the 5% significance level.
Conduct a hypothesis test for the ratio of two population variances.
Construct a confidence interval for the ratio of two population variances.
Discuss features of the F distribution.
Conduct a hypothesis test for the population variance.
Construct a confidence interval for the population variance.
Discuss features of the x distribution.P-69
In order to conduct a hypothesis test of the population variance, you c o m p u te s2 = 75 from a sample of 21 observations drawn from a normally distributed population.Use the critical value approach to conduct the following tests P-399 a. Hos 50; Ho> 50 b. Ho =50; Ho 50
Find the value x for which: P-399 0.005 a. P(xx) b. P(xx) = 0.01 c. C. P
Find the value x for which: P-399 a. P(xx)=0.025 b. P(x)=0.05 c. P
FILE (Use Excel) Adidas revenues (in millions o f €) in Asia and Latin America for the years 200 5 through 20 0 9 are sh o w n in th e accom panying table; th e data, labeled Adidas Revenues, are also available on the text website.2005 2006 2007 2008 2009 Asia 1,523 2,020 2,254 2,662 2,614 Latin
F IL E (Use Excel) Barbara Dwyer, the manager at Lux Hotel, makes every effort to ensure that customers attempting to make phone reservations do not have to wait too long to speak with a reservation specialist. Since the hotel accepts phone reservations 24 hours a day, Barbara is especially
Annual growth rates for individual firms in the toy industry tend to fluctuate dramatically, depending on consumers'tastes and current fads. Consider the following growth rates(in percent) for two companies in this industry, Hasbro and Mattel.Year 2005 2006 2007 2008 2009 Hasbro 3.0 2.1 21.8 4.8
FILE (Use Excel) The following table presents the returns of Fidelity's Select Automotive Fund; the data are also available on the text website, labeled A u to m o tive. This mutual fund invests primarily in companies engaged in the manufacturing, the marketing, or the sales of automobiles, trucks,
A financial analyst maintains that the risk, measured by the variance, of investing in emerging markets is more than 280(% )2. Data on 20 stocks from emerging markets revealed the following sample results: and s2 = 361 (%)2.Assume that the returns are normally distributed.a. Specify the competing
FILE Access the data labeled R e n ta ls on the text w ebsite that in clu d es m o n th ly rents o f a t w o - b e d r o o m a p a r tm e n t in tw o cam pus towns: Ann Arbor, Michigan, and Davis, California.Davis, California, is kn ow n to have higher rents than Ann Arbor, M ichigan; h ow ever, it
FIL E (U se Excel) A variety o f p a c k a g in g so lu tio n s ex ist for products th at m u st b e kept within a specific tem p eratu re range. Cold chain distribution is particularly useful in th e food and pharm aceutical industries. A packaging com pany is trying o u t a n e w p ack agin g
F I L E (Use Excel) The m onthly closing stock prices (rounded to th e nearest dollar) for Starbucks Corp. and Panera Bread Co. for th e first six m o n th s o f 2 0 1 0 are rep o rted in th e fo llo w in g ta b le. The data are also availab le o n t h e tex t w ebsite, labeled M o n th ly Stock
The follow ing tab le sh o w s th e annual returns (in percent) for Fidelity's Electronic and Utilities funds.Year E lectro nic U tilitie s 2005 13.23 9.36 2006 1.97 32.33 2007 2.77 21.03 2008 − 50.00 − 35.21 2009 81.65 14.71 Source: w w w .fin a n c e .y a h o o .c o m .U sing t h e critical v
Two basketball players on a sch ool tea m are working hard o n c o n s is t e n c y o f th eir p e r fo r m a n c e . In particular, t h e y are h o p in g to bring d o w n t h e va r ia n c e o f th eir scores. T he c o a c h b e lie v e s th a t t h e players are n o t eq u a lly c o n s iste n t
A firm h as ju s t d e v e l o p e d a n e w c o s t -r e d u c in g t e c h n o l o g y for producing a certain rep lacem en t part for autom obiles.Since a replacem ent part m ust be produced within close specifications in order for it to b e a c c e p ta b le to cu stom ers, the n ew
C o n sid er t h e fo llo w in g c o m p e t i n g h y p o t h e s e s a n d relev a n t su m m ary statistics:H0: σ2 1 /σ 2 2 ≥ 1 HA: σ2 1 /σ2 2 < 1 Sam ple 1: s 21 = 1 ,3 1 5 a n d n 1 = 17 Sam ple 2 : s21 = 1 ,5 2 3 a n d n2 = 19 C o n d u c t th is left-tailed h y p o t h e s i s t e s t
Consider th e follow ing co m p e tin g h y p o th eses and relevant sum m ary statistics:H0: σ21/σ22 = 1 HA: σ21/σ22 ≠ 1 A ssum e that the tw o populations are normally distributed.a. Using th e p -value approach, co n d u ct this hyp othesis test at th e 5% significance level.b. Confirm
Consider th e following m easures based on independently drawn samples from normally distributed populations:S a m p l e 1: s 21 = 2 2 0 , a n d n 1 = 2 0 Sa m p le 2: s 22 = 196, a n d n2 = 15 P-399a. C on str u c t a 95% interval e s t im a t e o f t h e ratio o f t h e population variances.b. U
C o n s tr u c t a 9 0 % interval e s t i m a t e o f t h e ratio o f t h e population variances using the following results from two independently drawn samples from normally distributed populations. P-399
U se t h e F t a b l e t o a p p r o x i m a t e t h e f o l l o w i n g probabilities.PLO5
Find th e v a lu e x for w hic h: PLO4
F IL E (Use Excel) While the housing market has not recovered, real estate investment in college towns continues to promise good returns (The Wall Street Journal, September 24, 2010). With rents holding up, this is good news for investors but the same cannot be said for students. There also tends
FILE (Use Excel) A ccess th e m iles per gallon (m pg) data on th e text w e b site labeled MPG.a. State th e null and th e alternative h y p o th e se s in order to test w h e th e r or n o t th e variance o f m p g differs from 62 m p g 2.b. Calculate th e relevant te st statistic.c. U se Excel's
FILE (U se Excel) A realtor in M ission Viejo, California, b eliev es that th e standard deviation o f h o u se prices is m ore than 100 units, w here each unit equals $1,000. A ssum e hou se prices are normally distributed.a. Sta te t h e null a n d t h e a lternative h y p o t h e s e s for t h e
India Fund, Inc. (IFN) is a d o s e - e n d e d e q u it y m u tual fu nd launched by the Blackstone Group, Asset M anagem ent Arm. A lth ou gh it prom ises im pressive returns, it d o e s s o at t h e c o s t o f g r ea ter risk. An an a ly st w o u ld like t o t e s t if th e varian ce o f t h e
A restaurant o w n er is con cern ed a b o u t th e con sisten cy of b u sin e s s. He w a n t s t o d e t e r m in e if t h e s ta n d a r d d e v ia tio n o f t h e profits for e a c h w e e k is less th an $ 3 0 0 . The profits from last w e e k are listed b elo w (in dollars). A ssu m e that
The m a n a g er o f a su perm ark et w o u ld like th e variance o f t h e w a i t i n g t i m e s o f t h e c u s t o m e r s n o t t o e x c e e d 3 m in u tes-sq u ared . Sh e w o u ld ad d a n e w cash register if th e v a rian ce e x c e e d s this th re sh o ld . S h e regularly ch eck s th
The follow ing tab le s h o w s th e annual returns (in percent) for th e Vanguard Energy Fund from 200 5 through 2009.Year E nergy 2005 44.60 2006 19.68 2007 37.00 2008 − 42.87 2009 38.36 Source: www.finance.yahoo.com .a. Calculate th e poin t estim ate o f σ .b. C on str u c t a 95% c o n f i
A consum er advocacy group is concerned about the variability in the cost o f prescription m edication. The group surveys e ight local pharmacies and obtains the follo w in g prices fo r a particular brand o f m edication:$25.50 32.00 33.50 28.75 29.50 35.00 27.00 29.00a. C alculate t h e p o in t
A replacem ent part fo r a m achine m ust be produced w ith in close specifications in order fo r it to be acceptable to customers. Suppose the sample variance fo r 20 parts turns o u t to b e s2 = 0.03.a. C onstruct a 95% confidence interval o f the population variance.b. Production specifications
A research analyst is exam ining a stock fo r possible inclusion in his client's p o rtfolio. Over a 10-year period, the sample mean and the sample standard deviation o f annual returns on the stock were 20% and 15%, respectively. The client w ants to know if the risk, as measured by the standard
You w ould like to test the claim th a t the variance o f a norm ally distributed population is m ore than 2 squared units. You draw a random sample o f 10 observations as 2 , 4, 1 , 3 , 2 , 5 , 2 , 6 , 1 , 4. A t α = 0.10, test the above claim using(a) the p -value approach and (b) the critical
The following values are drawn from a normal population.20 29 32 27 34 25 30 31a. Calculate the point estimates of the population variance and the population standard deviation.b. Compute a 95% confidence interval for the population variance and the population standard deviation. P-399

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