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Statistics For Business Decision Making And Analysis 2nd Edition Robert Stine, Dean Foster - Solutions

Which, if any, of these combinations of an X-bar chart and an S-chart suggest a problem? If there€™s a problem, did you find it in the X-bar chart, the S-chart, or both?
1. A sampling distribution describes the variability among average weights from day to day. 2. Before using a normal model for the sampling distribution of the average package weights, the manager must confirm that weights of individual packages are normally distributed. 3. A Type I error occurs if
1. y̅ + 2se (y̅)2. ŷ ± se (p̂)3. 2se (X-bar)4. N (μ, σ2 / n)5. s / √n6. σ / √n7. 1 / (0.05)28. [0,1]9. √ p̂ (1 – p̂) / n10. t0.025 n–1(a) Sampling distribution of X–bar(b) Margin of error(c) 100% confidence interval for p(d) Estimated standard
1. All other things the same, a 90% confidence interval is shorter than a 95% confidence interval. 2. Ninety-five percent z-intervals have the form of a statistic plus or minus 3 standard errors of the statistic. 3. By increasing the sample size from n = 100 to n = 400, we can reduce the margin of
1. If the 95% confidence interval for the number of moviegoers who purchase from the concession stand is 30% to 45%, then fewer than half of all moviegoers do not purchase from the concession stand. 2. If zero lies inside the 95% confidence interval for m, then zero is also inside the 99%
Convert these confidence intervals. (a) [11 pounds to 45 pounds] to kilograms [1 pound = 0.453 kilogram] (b) [$2,300 to $4,400] to yen (Use the exchange rate of $1= ¥ 116.3.) (c) [$79.50 to $101.44] minus a fixed cost of $25 (d) [$465,000 to $729,000] for total revenue of 25 retail stores to a
Convert these confidence intervals. (a) [14.3 liters to 19.4 liters] to gallons (1 gallon = 3.785 liters) (b) [€234 to €520] to dollars (Use the exchange rate 1 dollar = 0.821 euro.) (c) 5% of [$23,564 to $45,637] (d) 250 items at a profit of [$23.4 to $32.8] each (Give the interval for the
Which is shorter, a 95% z-interval for μ or a 95% t-interval for μ? Is one of these always shorter, or does the outcome depend on the sample?
The clothing buyer for a department store wants to be sure the store orders the right mix of sizes. As part of a survey, she measured the height (in inches) of men who bought suits at this store. Her software reported the following confidence interval: With 95.00% confidence, 70.8876 < μ <
Data collected by the human resources group at a company produced this confidence interval for the average age of MBAs hired during the past recruiting season. With 95.00% confidence, 26.202 6 μ 6 28.844 (a) Explain carefully what the software output means. (b) What is the margin of error for this
To prepare a report on the economy, analysts need to estimate the percentage of businesses that plan to hire additional employees in the next 60 days.(a) How many randomly selected employers must you contact in order to guarantee a margin of error of no more than 4%?(b) If analysts believe that at
A political candidate is anxious about the outcome of the election. (a) To have his next survey result produce a 95% confidence interval with margin of error of no more than 0.025, how many eligible voters are needed in the sample? (b) If the candidate fears that he’s way behind and needs to save
The Basel II standards for banking specify procedures for estimating the exposure to risk. In particular, Basel II specifies how much cash banks must keep on hand to cover bad loans. One element of these standards is the following formula, which expresses the expected amount lost when a borrower
Catalog sales companies such as L.L. Bean encourage customers to place orders by mailing seasonal catalogs to prior customers. The expected profit from each mailed catalog can be expressed as the product Expected profit = p × D × S where p is the probability that the customer places an order, D
Find the appropriate percentile from a t-distribution for constructing the following confidence intervals: (a) 90% t-interval with n = 12 (b) 95% t-interval with n = 6 (c) 99% t-interval with n = 15
Consider each situation described below. Identify the population and the sample, explain what the parameter p or μ represents, and tell whether the methods of this chapter can be used to create a confidence interval. If so, find the interval. (a) The service department at a new car dealer checks
Consider each situation. Identify the population and the sample, explain what p or μ represents, and tell whether the methods of this chapter can be used to create a confidence interval. If so, indicate what the interval would say about the parameter. (a) A consumer group surveys 195 people who
Hoping to lure more shoppers downtown, a city builds a new public parking garage in the central business district. The city plans to pay for the structure through parking fees. During a two-month period (44 weekdays), daily fees collected averaged $1,264 with a standard deviation of $150. (a) What
Suppose that for budget planning purposes the city in Exercise 39 needs a better estimate of the mean daily income from parking fees. (a) Someone suggests that the city use its data to create a 95% confidence interval instead of the 90% interval first created. Would this interval be better for the
A sample of 150 calls to a customer help line during one week found that callers were kept waiting on average for 16 minutes with s = 8. (a) Find the margin of error for this result if we use a 95% confidence interval for the length of time all customers during this period are kept waiting. (b)
A sample of 300 orders for take-out food at a local pizzeria found that the average cost of an order was $23 with s = $15. (a) Find the margin of error for the average cost of an order. (b) Interpret for management the margin of error. (c) If we need to be 99% confident, does the confidence
A book publisher monitors the size of shipments of its textbooks to university bookstores. For a sample of texts used at various schools, the 95% confidence interval for the size of the shipment was 250 ± 45 books. Which, if any, of the following interpretations of this interval is/are
A catalog sales company promises to deliver orders placed on the Internet within three days. Follow-up calls to randomly selected customers show that a 95% confidence interval for the proportion of all orders that arrive on time is 88% ± 6%. What does this mean? Are the following conclusions
Find the 95% z-interval or t-interval for the indicated parameter.(a) μ x̅ = 152, s = 35, n = 60(b) μ x̅ = 8, s = 75, n = 25(c) p p̂ = 0.5, n = 75(d) p p̂ = 0.3, n = 23
Show the 95% z-interval or t-interval for the indicated parameter.(a) μ x̅ = -45, s = 80, n = 33(b) μ x̅ = 255, s = 16, n = 21(c) p p̂ = 0.25, n = 48(d) p p̂ = 0.9, n = 52
Direct mail advertisers send solicitations (junk mail) to thousands of potential customers hoping that some will buy the product. The response rate is usually quite low. Suppose a company wants to test the response to a new flyer and sends it to 1,000 randomly selected people. The company gets
Not all junk mail comes from businesses. Internet lore is full of familiar scams, such as the desperate foreigner who needs your help to transfer a large amount of money. The scammer sends out 100,000 messages and gets 15 replies. Can the scam artist make a 95% confidence interval for the
A package of light bulbs promises an average life of more than 750 hours per bulb. A consumer group did not believe the claim and tested a sample of 40 bulbs. The average lifetime of these 40 bulbs was 740 hours with s = 30 hours. The manufacturer responded that its claim was based on testing
In Fall 2011, the Wall Street Journal reported that 44% of smartphone purchases made by people with incomes between $35,000 to $50,000 were Android phones.16 (a) If the story is based on a sample of 200 purchases, then should we conclude that Android phones were getting less than half of the market
Fireman’s Fund commissioned an online survey of 1,154 wealthy homeowners to find out what they knew about their insurance coverage. (a) When asked whether they knew the replacement value of their home, 63% replied yes. In this case, should Fireman’s Fund conclude that more than half of wealthy
Click fraud has become a major concern as more and more companies advertise on the Internet. When Google places an ad for a company with its search results, the company pays a fee to Google each time someone clicks on the link. That’s fine when it’s a person who’s interested in buying a
Philanthropic organizations, such as the Gates Foundation, care about the return on their investment, too. For example, if a foundation spends $7,000 for preschool education of children who are at risk, does society get a reasonable return on this investment? A key component of the social benefit
A phone company launched an advertising program designed to increase the number of minutes of long-distance calls made by customers. To get a sense of the benefits of the program, it ran a small test of the promotion. It first selected a sample of 100 customers of the type being targeted by the
An auto manufacturer leases cars to small businesses for use in visiting clients and other business travel. The contracted lease does not specify a mileage limit and instead includes a depreciation fee of $0.30 per mile. The contract includes other origination, maintenance, and damage fees in
1. One-sided null hypothesis2. Common symbols for the alternative hypothesis3. Maximum tolerance for incorrectly rejecting H04. Number of standard errors that separate an observed statistic from the boundary of H05. Number of estimated standard errors that separate an observed statistic from the
1. The appropriate null hypothesis for testing the profitability of the new design sets μ0 = +80. 2. The appropriate null hypothesis for testing the profitability of the new design is H0: μ ≤ μ0. 3. If the a-level of the test is α = 0.05, then there is at most a 5% chance of incorrectly
1. If H0 holds, then p̂ in the sample will be less than 0.4. 2. By setting a small a-level, the accounting firm reduces the chance of a test indicating that it should add this new service even though it is not profitable. 3. If p̂ is larger than 0.4, a test will reject the appropriate null
A pharmaceutical company is testing a newly developed therapy. If the therapy lowers the blood pressure of a patient by more than 10 mm, it is deemed effective.16 What are the natural hypotheses to test in a clinical study of this new therapy?
A chemical firm has been accused of polluting the local river system. State laws require the accuser to prove the polluting by a statistical analysis of water samples. Is the chemical firm worried about a Type I or a Type II error?
The research labs of a corporation occasionally produce breakthroughs that can lead to multibillion-dollar blockbuster products. Should the managers of the labs be more worried about Type I or Type II errors?
Modern combinatorial chemistry allows drug researchers to explore millions of products when searching for the next big pharmaceutical drug. An analysis can consider literally hundreds of thousands of compounds. Suppose that none of 100,000 compounds in reality produces beneficial results. How many
Consider the following test of whether a coin is fair. Toss the coin three times. If the coin lands either all heads or all tails, reject H0: p = 1 / 2. (The p denotes the chance for the coin to land on heads.) (a) What is the probability of a Type I error for this procedure? (b) If p = 3 / 4, what
A consumer interest group buys a brand-name kitchen appliance. During its first month of use, the appliance breaks. The manufacturer claims that 99% of its appliances work for a year without a problem. (a) State the appropriate null hypothesis that will facilitate a hypothesis test to analyze this
A jury of 12 begins with the premise that the accused is innocent. Assume that these 12 jurors were chosen from a large population, such as voters. Unless the jury votes unanimously for conviction, the accused is set free.(a) Evidence in the trial of an innocent suspect is enough to convince half
To demonstrate that a planned commercial will be cost effective, at least 60% of those watching the programming need to see the commercial (rather than switching stations or using a digital recorder to skip the commercial). Typically, half of viewers watch the commercials. It is possible to measure
A consultant claims that by following his advice, an insurance-processing center can reduce the time required to process a claim for storm damage from the current average length of 6.5 to 5 work-days. He claims that his method obviously works so H0: μ ≤ 6.5. He says he can save the insurer
The Human Resources (HR) group gives job applicants at a firm a personality test to assess how well they will fit into the firm and get along with colleagues. Historically, test scores have been normally distributed with mean m and standard deviation σ = 25. The HR group wants to hire applicants
A test of filtering software examined a sample of n = 100 messages. If the filtering software reduces the level of spam to 15%, this test only has a 33% chance of correctly rejecting H0: p ≥ 0.20. Suppose instead of using 100 messages, the test were to use n = 400. (a) In order to obtain a
An appliance manufacturer stockpiles washers and dryers in a large warehouse for shipment to retail stores. Some appliances get damaged in handling. The long-term goal has been to keep the level of damaged machines below 2%. In a recent test, an inspector randomly checked 60 washers and discovered
The electronic components used to assemble a cellular phone have been exceptionally reliable, with more than 99.9% working correctly. The head of procurement believes that the current supplier meets this standard, but he tests components just the same. A test of a sample of 100 components yielded
A company that stocks shelves in supermarkets is considering expanding the supply that it delivers. Items that are not sold must be discarded at the end of the day, so it only wants to schedule additional deliveries if stores regularly sell out. A break-even analysis indicates that an additional
Field tests of a low-calorie sport drink found that 80 of the 100 who tasted the beverage preferred it to the regular higher-calorie drink. A break-even analysis indicates that the launch of this product will be profitable if the beverage is preferred by more than 75% of all customers.(a) State the
The management of a chain of hotels avoids intervening in the local management of its franchises unless problems become far too common to ignore. Management believes that solving the problems is better left to the local staff unless the measure of satisfaction drops below 33%. A survey of 80 guests
An importer of electronic goods is considering packaging a new, easy-to-read instruction booklet with DVD players. It wants to package this booklet only if it helps customers more than the current booklet. Previous tests found that only 30% of customers were able to program their DVD player. An
A variety of stores offer loyalty programs. Participating shoppers swipe a bar-coded tag at the register when checking out and receive discounts on certain purchases. Stores benefit by gleaning information about shopping habits and hope to encourage shoppers to spend more. A typical Saturday
Brand managers become concerned if they discover that customers are aging and gradually moving out of the high-spending age groups. For example, the average Cadillac buyer is older than 60, past the prime middle years that typically are associated with more spending. Part of the importance to
Refer to the analysis of shoppers in Exercise 45.(a) If several of those participating in the loyalty program are members of the same family, would this cause you to question the assumptions that underlie the test in this question?(b) Several outliers were observed in the data for the loyalty
Refer to the analysis of car buyers in Exercise. (a) Suppose the distribution of the ages of the buyers of the Cadillac Escalade is skewed. Does this affect the use of a normal model as the sampling distribution? How skewed can the data become without preventing use of the t-test? (b) The
Refer to the analysis of shoppers in Exercise 45. If the population mean spending amount for shoppers in the loyalty program is $135 (with Ïƒ = $40), then what is the probability that the test procedure used in this question will fail to reject H0?
Refer to the analysis of car buyers in Exercise 46. If the population mean age for purchasers of the Cadillac Escalade is 50 years (with σ = 25 years), then what is the probability that the test procedure used in this question will fail to reject H0?
Banks frequently compete by adding special services that distinguish them from rivals. These services can be expensive to provide. The bank hopes to retain customers who keep high balances in accounts that do not pay large interest rates. Typical customers at this bank keep an average balance of
Headhunters locate candidates to fill vacant senior positions in companies. These placement companies are typically paid a percentage of the salary of the filled position. A placement company that specializes in biostatistics is considering a move into information technology (IT). It earns a fee of
Performance Tires plans to engage in direct mail advertising. It is currently in negotiations to purchase a mailing list of the names of people who bought sports cars within the last three years. The owner of the mailing list claims that sales generated by contacting names on the list will more
A specialist in the Human Resources department of a national hotel chain is looking for ways to improve retention among hotel staff. The problem is particularly acute among those who maintain rooms, work in the hotel restaurant, and greet guests. Within this chain, among those who greet and
1. Plot used for visual comparison of results in two (or more) groups2. Difference between the averages in two samples3. Difference between the averages in two populations4. Name given to the variable that specifies the treatments in an experiment5. Estimate of the standard error of the difference
1. The null hypothesis from a break-even analysis should include the possibility that the methods are equally profitable. 2. A one-sided test of H0: m1 - μ2 ≤ 10 rejects H0 if 10 lies outside of the 95% confidence interval for μ1 - μ2. 3. If the standard two-sample t-test rejects H0: μ1 - μ2
1. The t-statistic in a two-sample test does not depend on the units of the comparison. (We could, for example, measure the data in dollars or cents.)2. If the boxplots of the data for the two groups overlap, then the two means are not significantly different.3. If the confidence interval for m1
A busy commuter is concerned about the time she spends in traffic getting to the office. She times the drive for a couple of weeks and finds that it averages 40 minutes. The next day, she tries public transit and it takes 45 minutes. The next day, she’s back on the roads, convinced that driving
Doctors tested a new type of contact lens. Volunteers who normally wear contact lenses were given a standard type of lens for one eye and a lens made of the new material for the other. After a month of wear, the volunteers rated the level of perceived comfort for each eye. (a) Should the new lens
Members of a sales force were randomly assigned to two management groups. Each group employed a different technique for motivating and supporting the sales team. Let’s label these groups A and B, and let μ A and μ B denote the mean weekly sales generated by members of the two groups. The 95%
Management of a company divided its sales force into two groups. The situation is precisely that of the previous exercise, only now a manager decided the assignment of the groups. The 95% confidence interval for μ A – μ B was found to be [$500, $2,200].(a) Does the lack of randomized assignment
Many advocates for daylight savings time claim that it saves money by reducing energy consumption. Generally it would be hard to run an experiment to test this claim, but as fortune would have it, counties in Indiana provided an opportunity. Until 2006, only 15 of the 92 counties in Indiana used
Managers of a national retail chain want to test a new advertising program intended to increase the total sales in each store. The new advertising requires moving some display items and making changes in lighting and deco-ration. The changes can be done overnight in a store. How would you recommend
The recommendations of respected wine critics such as Robert M. Parker, Jr. have a substantial effect on the price of wine. Vintages that earn higher ratings command higher prices and spark surges in demand. These data are a sample of ratings of wines selected from an online Web site from the 2000
A factory hiring people for tasks on its assembly line gives applicants a test of manual dexterity. This test counts how many oddly shaped parts the applicant can install on a model engine in a one-minute period. Assume that these tested applicants represent simple random samples of men and women
These data indicate the prices of 155 used BMW cars. Some have four-wheel drive (the model identified by the Xi type) and others two-wheel drive (the model denoted simply by the letter i).(a) If we treat the data as samples of the typical selling prices of these models, what do you conclude? Do
These data give the sales volume (in dollars per square foot) for 37 retail outlets specializing in women’s clothing in 2006 and 2007. Did sales change by a statistically significant amount from 2006 to 2007?
Based on data collected in 2010, 23 percent of women wanted to buy a Google Android smart phone or tablet. Among men, 33 percent were interested in an Android purchase next. The survey contacted 240 women and 265 men. (a) Might the comparison between these two samples be confounded with a hidden
Internet search engines report many hits, but getting on the first page is critical for a business. A study surveyed 1,232 people from a U.S. online consumer panel in 2002 and independently surveyed a second panel of 1,137 in 2009. Analysts found that 62% of those surveyed in 2009 clicked on a
A retail chain is considering installing de-vices that resemble cameras to deter shoplifting. The devices only look like cameras, saving the expense of wiring and recording video. To test the benefit of this decoy system, it picked 40 stores, with half to get the decoy and the other half to serve
A golf equipment manufacturer would like to convince members of a club that its golf balls travel farther than those of a competitor, even for weekend golfers. For the comparison, twelve golfers randomly selected from the club to each drive a ball from this manufacturer and from the rival. The
A cosmetics firm uses two different ship-ping companies. Shipper A is more expensive, but managers believe that fewer shipments get damaged than when shipped the current shipper used by the firm, Shipper B. To compare the shippers, the company devised the following comparison. The next 450
High turnover of employees is expensive for firms. The firm not only loses experienced employees, it must also hire and train replacements. A firm is considering several ways to improve its retention (the proportion of employees who continue with the firm after 2 years). The currently favored
Anyone who’s ever watched late-night TV knows how many people want to lose weight the easy way. On the basis of recent medical studies, there may be such a thing. Glaxo Smith Kline bought the drug Orlistat with the hopes of turning it into a modern miracle. Results in prior clinical trials had
Statistical analyses are often featured in lawsuits that allege discrimination. Two-sample methods are particularly common because they can be used to quantify differences between the average salaries of, for example, men and women.A lawsuit filed against Wal-Mart in 2003 alleged that the retailer
1. A bank audited 100 randomly selected transactions of a newly hired cashier and found that all 100 were done correctly. What is the 95% confidence interval for the cashier’s probability of an error? 2. In order to be 95% confident that the incidence of fraud among tax returns is less than 1 in
1. A product line is sold in 15 different configurations of packaging. How does the large number of package types influence the value of the chi-squared statistic? 2. Why are chi-squared statistics not directly comparable between tables of different dimensions when the null hypothesis of
1. Number of degrees of freedom in the chi-squared test of independence in a 2 × 2 table 2. Number of constraints on frequencies in the chi-squared test of goodness of ft of a binomial distribution 3. P-value if x2 = 9.488 when testing for independence in a 3 × 3 table 4. P-value if x2 = 16.812
1. The chi-squared test of independence only detects linear association between the variables in a contingency table. 2. A statistically significant x2 in the test of independence implies a causal relationship between the variables that define a contingency table. 3. The expected size of the
1. Small p-values of the chi-squared test of independence indicate that the data have small amounts of dependence. 2. Small values of x2 imply that the null hypothesis in a chi-squared test is true. 3. The chi-squared test of independence requires at least 5 to 10 observations in each cell of the
(a) Does this stacked bar chart suggest that the chi-squared test of independence will be statistically significant? Explain why or why not.(b) What are the degrees of freedom in the chi-squared test of independence for these data? (c) What would a mosaic plot show you that you cannot tell from the
(a) Does this stacked bar chart suggest that the chi-squared test of independence will be statistically significant? Explain why or why not.(b) What are the degrees of freedom in the chi-squared test of independence for these data?(c) Should seeing a mosaic plot of these data possibly change your
The following contingency table breaks down a month of customer complaints received by a retailer. Some of those complaining are long-term customers, whereas the rest are recent. There are four types of complaints.(a) What would it mean to the retailer if customer status and complaint type were
A mobile phone service provider randomly samples customers each year to measure current satisfaction with the service provided. The following table summarizes a portion of the survey, with 100 customers sampled each year. Customers are labeled €œvery satisfied€ if they rate
These data count the number of male and female shoppers who accept or reject a discounted offer in return for supplying a retailer with an email address. Consider using these data to test the null hypothesis that gender and acceptance are independent (H0). Find the (a) Degrees of freedom of x2. (b)
These data count the types of meals ordered by customers at two restaurants in a national chain. Consider using these data to test the null hypothesis that store and choice are independent (H0). Find the(a) Degrees of freedom of x2. (b) Expected number of customers who order beef at restaurant 1,
The following table shows counts of the number of days that employees were absent from a small manufacturing center. The null hypothesis is that the counts are uniformly distributed over the days of the week. Find the(a) Degrees of freedom of x2. (b) Expected number of days absent on Wednesday, if
The table shown with this question counts the number of calls that arrive at a telephone help desk during the hours of 1 to 3 P.M. on 5 weekdays. The company uses the same number of employees to staff the center for each of these days. Test the null hypothesis that the calls are uniformly
The human resources group regularly interviews prospective clerical employees and tests their skill at data entry. The following table shows the number of errors made by 60 prospective clerks when entering a form with 80 numbers. (Five clerks made 4 errors.) Test the null hypothesis that the number
A type of new car is offered for sale with 4 option packages. A customer can buy any number of these, from none to all 4. A manager proposes the null hypothesis that customers pick packages at random, implying the number of packages bought by a customer should be binomial with n = 4. This table

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