You work for a company that prepares and distributes frozen foods. The package claims a net weight of 14.5 ounces. A random sample of today’s production was weighed, producing the following data set: 14.43, 14.37, 14.38, 14.29, 14.60, 14.45, 14.16, 14.52, 14.19, 14.04, 14.31 A sample was also selected from yesterday’s production. The average was 14.46 and the standard deviation was 0.31. a. Estimate the mean weight you would have found had you been able to weigh all packages produced today. b. For a typical individual package produced yesterday, approximately how different was the actual weight from yesterday’s average? c. Find the 95% confidence interval for the mean weight for all packages produced today. d. Identify the hypotheses you would work with to test whether or not your claimed weight is correct, on average, today. e. Is there a significant difference between claimed and actual mean weight today? Justify your answer.
> A linear regression analysis has produced the following equation relating profits to hours of managerial time spent developing the past year’s projects at a firm: Profits= -$957+$85 × Number of hours a. According to this estimated relationship, how large
> Are top executives of larger companies paid significantly more than those of smaller companies? Consider data on CEO pay (dollars) and market capitalization (the total market value of stock, in $millions) for a sample of companies, as shown in Table 11.3
> Consider the weight and price of gold coins from Table 11.3.10. a. How strong is the association between weight and price for these coins? Please give both a number and its interpretation in words. b. Find the regression equation to predict price from we
> Gaining visibility for your products can be expensive, and television advertising during the Super Bowl is a good example, with a cost of nearly $2 million for a 30-s message. This high cost is due, in part, to the large number of Super Bowl viewers. Tab
> How predictable are advertising budgets from year to year? Consider the 2008 and 2009 advertising spending of selected firms as reported in Table 11.3.8. a. Summarize the strength of the year-to-year relationship in advertising budget by computing and in
> In the presidential election of 2000, a number of events occurred between the initial vote count of Nov.7 and the count as certified by the Florida Secretary of State following counting of absentee ballots, a machine recount, and a Florida Supreme Court
> Would it be better to multiply by the size of the frame used to select the random sample?
> Do separate histograms for Owen and Purcell agree with Billings’s contention that Owen spends more?
> Consider the expense ratio and the total one-year rate of return on the W&R family of mutual funds in Table 11.3.6. a. What percentage of the variation in rate of return is explained by expense ratio? Please provide both the name of the measure and i
> Using the donations database on the companion site, and using only people who made a donation in response to the current mailing, consider predicting the amount of a donation (named “Donation_D1” in the worksheet) from the percentage of households in the
> Using the donations database on the companion site, and using only people who made a donation in response to the current mailing, consider predicting the amount of a donation (named “Donation_D1” in the worksheet) from the percentage of households in the
> Consider the data set in Table 11.3.1, representing the ages (in years) and maintenance costs (in thousands of dollars per year) for five similar printing presses. a. Draw a scatterplot of this data set. What kind of relationship do you see? b. Find the
> Your bakery produces loaves of bread with “1 pound” written on the label. Here are weights of randomly sampled loaves from today’s production: 1.02,0.97, 0.98,1.10,1.00, 1.02,0.98, 1.03,1.03, 1.05, 1.02, 1.06 a. Find the 95% confidence interval for the m
> Your factory’s inventory level was determined at 12 randomly selected times last year, with the following results: 313, 891, 153, 387, 584, 162, 742, 684, 277, 271, 285, 845 a. Find the typical inventory level throughout the whole year, using the standar
> In a random sample of 725 selected for interview from your database of 13,916 customers, 113 said they are dissatisfied with your company’s service. a. Find the best estimate of the percentage of all customers in your entire database who are dissatisfied
> A cup of coffee is found to have only 72.8 milligrams of caffeine. Test (at the 5% level) whether the beans used could have come from the same population as those that generated the data in problem 47 of Chapter 9. Data from problem 47: The amount of c
> Repeat problem 49 for yet another product. For 158 outgoing consumers, the average rating was 7.93, and the standard deviation was 2.03. For 224 shy consumers, the average rating was 8.11, and the standard deviation was 1.55. Data from Problem 49: You
> Repeat the previous problem for a different product. For 142 outgoing consumers, the average rating was 7.28, and the standard deviation was 2.18. For 277 shy consumers, the average rating was 8.78, and the standard deviation was 1.32. Data from Problem
> Is it proper to multiply the average order size, $42.33, by the number of addresses (1,300,000) in the target mailing?
> Some of your advertisements seem to get no reaction, as though they are being ignored by the public. You have arranged for a study to measure the public’s awareness of your brand before and after viewing a TV show that includes the advertisement in quest
> You are analyzing the results of a consumer survey of a product, rated on a scale from 1 to 10. For the 130 consumers who described themselves as “outgoing,” the average rating was 8.36, and the standard deviation was 1.82. For the 218 “shy” consumers, t
> Your Detroit division produced 135 defective parts out of the total production of 983 last week. The Kansas City division produced 104 defectives out of 1,085 produced during the same time period. a. Find the percent defective for each division and compa
> Consider the weights for two samples of candy bars, before and after intervention, from Table 5.5.4. a. Is this a paired or an unpaired situation? b. Find the 95% confidence interval for the population mean difference in weight per candy bar (after minus
> To help you decide which of your two current suppliers deserves the larger contract next year, you have rated a random sample of plastic cases from each one. The data are a composite of several measurements, with higher numbers indicating higher quality
> There are two manufacturing processes, old and new, that produce the same product. The defect rate has been measured for a number of days for each process, resulting in the following summaries (Table 10.7.10). a. By how much would we estimate that the de
> An advertising study interviewed six randomly selected people in each of two cities, recording each person’s level of preference for a new product (Table 10.7.9). a. Is this a paired or an unpaired two-sample problem? b. Find the averag
> Child care is one of life’s necessities for working parents. Monthly rates per child at a sample of family day care centers in the North Seattle area are shown in Table 10.7.8. The Laurelhurst area is considered to be a highly desirable
> To understand your competitive position, you have examined the reliability of your product as well as the reliability of your closest competitor’s product. You have subjected each product to abuse that represents about a yearâ
> A group of experts has rated your winery’s two best varietals. Ratings are on a scale from 1 to 20, with higher numbers being better. The results are shown in Table 10.7.6. a. Is this a paired or unpaired situation? Why? b. Find the ave
> Are there useful results here? Which ones are useful? Are they sufficient, or is further study needed?
> Stress levels were recorded during a true answer and a false answer given by each of six people in a study of lie detecting equipment, based on the idea that the stress involved in telling a lie can be measured. The results are shown in Table 10.7.5. a.
> Why do firms change ownership? One possible reason for acquisitions is that the new owners expect to be able to manage the operations more efficiently than the current management. This theory leads to testable hypotheses. For example, it predicts that pr
> Last year you received an average of 129.2 complaints (i e, individual items to be fixed under warranty) per new car sold, with a standard deviation of 42.1 complaints based on 3,834 new cars sold. This year you have set up a quality assurance program to
> Your broker achieved a rate of return of 18.3% on your portfolio last year. For a sample of 25 other brokers in the area, according to a recent news article, the average rate of return was 15.2% with a standard deviation of 3.2% (as percentage points). a
> World investments markets were highly volatile in 1998. Table 10.7.4 shows one-year rates of return on closed end mutual funds that specialize in in come from international sources. a. Do the rates of return of these closed-end world income funds, as a g
> Selected mutual funds that practice socially aware investing, with year-to-date rates of return, are shown in Table 10.7.3. On average, these funds lost value in the first half of 2010, in the sense that their average rate of return was negative. However
> Do employees take more sick leave in the year before retirement? They may well have an incentive to do so if their accumulated paid sick leave (the number of days they are entitled to be away with full pay) is about to expire. Indeed, this appears to hap
> Dishwasher detergent is packaged in containers that claim a weight of 24 ounces. Although there is some variation from one package to another, your policy is to ensure that the mean weight for each day’s production is slightly over 24 ounces. A random sa
> You are supervising an audit to decide whether or not any errors in the recording of account transactions are “material errors.” Each account has a reported balance, whose accuracy can be verified only by careful and costly investigation; the account’s e
> The goal of your marketing campaign is for more than 25% of supermarket shoppers to recognize your brand name. A recent survey of 150 random shoppers found that 21.3% recognized your brand name. a. It might be argued that the burden of proof is to show t
> How might you explain differences among averages in the results?
> Managers perceived employee stock ownership as having a significant positive effect on product quality. As part of that same study, managers were also asked to rate the effect of employee stock ownership on unit labor cost.24 This effect, on a scale from
> Part of the assembly line will need adjusting if the consistency of the injected plastic becomes either too viscous or not viscous enough as compared with a value (56.00) your engineers consider reasonable. You will decide to adjust only if you are convi
> A recent poll of 1,423 randomly sampled likely voters shows your favorite candidate ahead, with 51.93% in favor. There are two candidates. Use hypothesis testing to infer to the larger group of all likely voters to see whether or not this indicates that
> A manufacturing process is considered to be “in control” if the long run mean weight of components produced is 0.20 kilograms, even though individual components may vary from this mean. Here are weights of a random sample of recently produced components:
> Regulations require that your factory provide convincing evidence that it discharges less than 25 milligrams of a certain pollutant each week, on average, over the long run. A recent sample shows weekly amounts of 13, 12, 10, 8, 22, 14, 10, 15, 9, 10, 6,
> Consider the dollar value (in thousands) of gifts returned to each of your department stores after the holiday season (Table 10.7.2): a. Compute the standard deviation. b. Interpret the standard deviation as a measure of the variation from one store to a
> Some frozen food dinners were randomly selected from this week’s production and destroyed in order to measure their actual calorie content. The claimed calorie content is 200. Here are the calorie counts for each dinner: 221, 198, 203, 223, 196, 202, 219
> Although your product, a word game, has a list price of $12.95, each stories free to set the price as it wishes. You have just completed a quick survey, and the marked prices at a random sample of stores that sell the product were as follows: $12.95, 9.9
> You are considering a new delivery system and wish to test whether delivery times are significantly different, on average, than your current system. It is well established that the mean delivery time of the current system is 2.38 days. A test of the new
> Do you agree that the follow-up mailings were a good idea?
> a. Perform a two-sided test at the 1% significance level for the previous problem and describe the result. b. State the p-value as either p>0.05, p
> As part of a decision regarding a new product launch, you want to test whether or not a large enough percentage (10 % or more) of the community would be interested in purchasing it. You will launch the product only if you find convincing evidence of such
> a. Why might a one-sided test be appropriate for the preceding problem? b. Identify the null and research hypotheses for a one sided test, using both words and mathematical symbols. c. Perform a one-sided test at the 5% significance level and describe th
> At a recent meeting, it was decided to go ahead with the introduction of a new product if “interested consumers would be willing, on average, to pay $20.00 for the product.” A study was conducted, with 315 random interested consumers indicating that they
> If the list price of the Eureka 4750A Bagged Upright Vacuum cleaner is $79.99, is the average price, based on the data from Table 9.6.1, significantly different from a 10% discount? Table 9.6.1: TABLE 9.6.1 Prices of the Eureka 4750A Bagged Upright
> Suppose that the target response rate was 4% when the current mailing was sent to the 20,000 people in the donations database on the companion site. a. Find the actual response rate represented by the 989 donations received in response to this mailing to
> View the 20,000 people in the donations database on the companion site as a random sample from a much larger group of potential donors. Determine whether or not the amount donated in response to the current mailing (named “Donation” in the database), on
> To help your restaurant marketing campaign target the right age levels, you want to find out if there is a statistically significant difference, on the average, between the age of your customers and the age of the general population in town, 43.1 years.
> Consider the quality scores measured for a random sample of agricultural produce: 16:7,17:9,23:5,13:8,15:9,15:2,12:9,15:7 a. Find the 95% confidence interval for the population mean quality. b. Find the 95% prediction interval for the quality of the next
> A random sample of 50 recent patient records at a clinic shows that the average billing per visit was $53.01 and the standard deviation was $16.48. a. Find the 95% confidence interval for the mean and interpret it. b. Find the 99% confidence interval. c.
> Do you agree that drawing a second sample was a good idea?
> So far at your new job, you have landed nine sales contracts with an average price of $3,782 and a standard deviation of $1,290. a. Identify a reasonable idealized population that this sample represents. b. If the distribution of sales prices is heavily
> You are concerned about waste in the newspaper publishing process. Previously, no measurements were made, although it is clear that frequent mistakes often require many pounds of newsprint to be thrown away. To judge the severity of the problem and to he
> Samples of rock taken from various places in a proposed mine have been analyzed. For each sample, a “rate of return” number has been computed that represents the profit obtained (by selling the refined metal at the current market price) as a percentage o
> As a basis for a brochure describing the speed of a new computer system, you have measured how long it takes the machine to complete a particular benchmark database program. Since the state of the disks in the database is constantly changing as records a
> A sample of 93 coils of sheet steel showed that the average length was 101.37 m, with a standard deviation of 2.67 m. a. Interpret the standard deviation in words; in particular, what is it measuring the variability of? b. Find the standard error. Interp
> A survey of your customers shows, to your surprise, that 42 out of 200 randomly selected customers were not satisfied with after-sale support and service. a. Find the summary statistics: the sample size, n; the sample percentage, p; and the standard erro
> An election poll shows your favorite candidate ahead with 52.443% of the vote, based on interviews with 921 randomly selected people. a.* Find the two-sided 95% confidence interval for the percentage of the population in favor of your candidate. b. Since
> Table 9.6.2 shows the 2015 performance of stocks recommended by Gene Marcial, whose list was published in Forbes in December 2014. a. Compute the average and briefly describe its meaning. b. Compute the standard deviation and briefly describe its meaning
> During a 1-week experiment, motion was added to in store sales displays at a random sample of your firm’s stores nationwide. The resulting sales increases for these products (compared to the week before) averaged $441.84, with a standard deviation of $68
> Out of 763 people chosen at random, 152 were unable to identify your product. a. Estimate the percentage of the population (from which this sample was taken) who would be unable to identify your product. b. Find the standard error of the estimate found i
> Should you lease or not?
> The following quotes for cleaning cost have been obtained from a random sample of 12 providers chosen from a much larger population, prior to awarding a contract for these services: $114,$154,$142,$132,$127,$145 $135,$138,$126,$142,$135,$124 a. Approxima
> Click-throughratesweremeasuredforeachof83mobile advertising campaigns, and showed an average rate of 2.38%, with a standard error of 0.134%. Please note that this is not a binomial situation because we are analyzing 83 percentage numbers and we do not kn
> Cost observations provided for 21 production situations have an average of $149.67 and a standard deviation of $38.85. a. Find and interpret the two-sided 95% confidence interval. b. Find the two-sided 99.9% confidence interval. c. Find the one-sided 95%
> View the 20,000 people represented in the donations database (on the companion site) as a sample from a much larger population. Of these 20,000 people, 989 made a donation in response to the current mailing. a. Find the 95% confidence interval for the po
> Randomly selected consumers in four cities have been interviewed as part of a study by a shoe retailer. Each consumer reported the number of pairs of shoes in his or her closet (each line represents one city) (Table 8.6.5): a. Estimate the mean number of
> Theaccountsofafirmhavebeenclassifiedinto56large accounts, 956 medium-sized accounts, and 16,246 small accounts. Each account has a book value (which is provided to you) representing the amount of money that is supposed to be in the account. Each account
> A poll involved interviews with 1,487 people and found that 42.3% of those interviewed were in favor of the candidate in question. The election will be held in 3 weeks. a. Approximately what percentage of the entire population would say they were in favo
> Here is a list of the dollar amounts of recent billings: $994, $307, $533, $443, $646, $148, $307, $524, $71, $973, $710, $342, $494 a. Find the average sale. What does this number represent? b. Find the standard deviation. What does this number represen
> Economists often make forecasts of future conditions. Consider the US unemployment rate for June 2015 as predicted in October 2014 as part of a survey of economists, as shown in Table 8.6.4. a. Find the average and the standard deviation. Briefly interpr
> Consider the percent change in revenues for the five largest soap and cosmetics firms as shown in Table 8.6.3. View this list as a (very small!) population with just N = 5 units. Consider drawing samples of size n = 2. a. Make a list of all possible samp
> How much money would you make if there were no costs of extraction? Would this be enough to retire?
> Consider the profits as a percent of revenue for a group of companies involved in petroleum and/or mining, as shown in Table 8.6.2. a. Construct a sampling frame, viewing this list as a population of large petroleum and/or mining-related firms. b. Draw a
> You have a factory with 40 production machines that are essentially identical, each producing a tame an daily rate of100productswithastandarddeviationof15.Youmay assume that they produce independently of one another. Consider the average daily production
> Yourrestaurantwillserve50dinnergroupstonight.Assume that the mean check size of dinner groups in general is $60, the standard deviation is $40, and the distribution is slightly skewed with a longer tail toward high values. a. Find the mean and standard d
> At a medical clinic, patient office visits are found to last a mean time of 17 min, with a standard deviation of 10 min. Assume that the probability distribution of time is independent from one patient to another. a. What is the approximate probability t
> Your automatic transmission factory has had some problems with quality. You have decided to gather information from tomorrow’s production for careful evaluation. For each of the following sampling methods, say if the procedure is good, acceptable, or unr
> You can invest in just one of four projects on a lot of land you own. For simplicity, you have modeled the payoffs (as net present value in today’s dollars) of the projects as discrete distributions. By selling the land, you can make $60,000 for sure. If
> Your company is hoping to fill a key technical position and has advertised in hopes of obtaining qualified applicants. Because of the demanding qualifications, the pool of qualified people is limited and Table 7.6.3 shows your subjective probabilities fo
> A TV system is expected to last for 50,000 hours before failure. Assume an exponential distribution for the time until failure. a. Is the distribution skewed or symmetric? b. What is the standard deviation of the length of time until failure? c. The syst
> In order to earn enough to pay your firm’s debt this year, you will need to be awarded at least two contracts. This is not usually a problem, since the yearly average is 5.1 contracts. You may assume a Poisson distribution. a. Find the probability that y
> You are planning to interview 350 consumers randomly selected from a large list of likely sales prospects, in order to assess the value of this list and whether you should assign salespeople the task of contacting them all. Assuming that 13% of the large
> Should you recommend that Wallace start looking for another job? If not, what do you suggest?
> A manufacturing process produces semiconductor chips with a known failure rate of 6.3%. Assume that chip failures are independent of one another. You will be producing 2,000 chips tomorrow. a. What is the name of the probability distribution of the numbe
> The length of time a system is “down” (ie, broken) is described(approximately) by the probability distribution in Table 7.6.2. Assume that these downtimes are exact. That is, there are three types of easily recognized
> Your firm has decided to interview a random sample of 10 customers in order to determine whether or not to change a consumer product. Your main competitor has already done a similar but much larger study and has concluded that exactly 86% of consumers ap
> Its been a bad day for the market, with 80% of securities losing value. You are evaluating a portfolio of 15 securities and will assume a binomial distribution for the number of securities that lost value. a.* What assumptions are being made when you use
> Suppose that 8% of the loans you authorize as vice president of the consumer loan division of a neighborhood bank will never be repaid. Assume further that you authorized 284 loans last year and that loans go sour independently of one another. a. How man
