Question: Fresh numbers from the U.S. Department

> Founded in February 2004, Facebook is a social utility that helps people communicate with their friends and family. In just six years, Facebook had acquired more than 500 million active users, of which 50% logged on to Facebook in any given day. In a sur

> You are considering two mutual funds as an investment. The possible returns for the funds are dependent on the state of the economy and are given in the accompanying table. You believe that the likelihood is 20% that the economy will be good, 50% that

> A study by the Massachusetts Community & Banking Council found that blacks, and, to a lesser extent, Latinos, remain largely unable to borrow money at the same interest rate as whites (The Boston Globe, February 28, 2008). The following contingency t

> According to a 2008 survey by the Pew Research Center, people in China are highly satisfied with their roaring economy and the direction of their nation (USA Today, July 22, 2008). Eighty-six percent of those who were surveyed expressed positive views of

> Consider a multinomial experiment with n = 400 and k = 3. The null hypothesis is H0: p1 = 0.60, p2 = 0.25, and p3 = 0.15. The observed frequencies resulting from the experiment are a. Specify the alternative hypothesis. b. Calculate the value of the te

> The quality manager believes there may be a relationship between the experience level of an inspector and whether a product passes or fails inspection. Inspection records were reviewed for 630 units of a particular product, and the number of units which

> A marketing agency would like to determine if there is a relationship between union membership and type of vehicle owned (domestic or foreign brand). The goal is to develop targeted advertising campaigns for particular vehicle brands likely to appeal to

> The following sample data reflect shipments received by a large firm from three different vendors and the quality of those shipments a. Specify the competing hypotheses to determine whether quality is associated with the source of the shipments. b. Con

> A market researcher for an automobile company suspects differences in preferred color between male and female buyers. Advertisements targeted to different groups should take such differences into account, if they exist. The researcher examines the most r

> According to an online survey by Harris Interactive for job site CareerBuilder.com (InformationWeek.com, September 27, 2007), more than half of IT workers say they have fallen asleep at work. The same is also true for government workers. Assume that the

> Given the following contingency table, conduct a test for independence at the 1% significance level. Variable A Variable B 1 2 3 4 1 120 112 100 110 2 127 115 120 124 3 118 115 110 124

> Given the following contingency table, conduct a test for independence at the 5% significance level. Variable A Variable B 1 2 1 23 47 32 53

> An investor considers investing $10,000 in the stock market. He believes that the probability is 0.30 that the economy will improve, 0.40 that it will stay the same, and 0.30 that it will deteriorate. Further, if the economy improves, he expects his inve

> An agricultural grain company processes and packages various grains purchased from farmers. A high-volume conveyor line contains four chutes at the end, each of which is designed to receive and dispense equal proportions of grain into bags. Each bag is t

> The quality department at an electronics company has noted that, historically, 92% of the units of a specific product pass a test operation, 6% fail the test but are able to be repaired, and 2% fail the test and need to be scrapped. Due to recent process

> An Associated Press/GfK Poll shows that 38% of American drivers favor U.S. cars, while 33% prefer Asian brands, with the remaining 29% going for other foreign cars (www.msnbc.com, April 21, 2010). A researcher wonders whether the preferences for cars hav

> Consider a multinomial experiment with n = 250 and k = 4. The null hypothesis to be tested is H0: p1 = p2 = p3 = p4 = 0.25. The observed frequencies resulting from the experiment are a. Specify the alternative hypothesis. b. Calculate the value of the

> A research analyst is examining a stock for possible inclusion in his client’s portfolio. Over a 10-year period, the sample mean and the sample standard deviation of annual returns on the stock were 20% and 15%, respectively. The client wants to know if

> Consider the following hypotheses: Find the p-value based on the following sample information, where the sample is drawn from a normally distributed population. a. s2 = 300; n = 25 b. s2 = 100; n = 25 c. Which of the above sample information enables us

> Adidas revenues (in millions of €) in the Greater China and Western Europe regions for the years 2011 through 2015 are shown in the accompanying table. Assume revenues are normally distributed. Source: Adidas Online Annual Reports. a.

> 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, Bar

> An automotive parts distributor wants to standardize its safety stock level for two parts, A and B. (“Safety stock” is the excess inventory carried above the expected demand level to provide protection against demand variability.) Consequently, the distr

> At Burger Joint, consistency in product and service is the new motto. Accordingly, management has invested in an automated French-fry dispenser to replace the manual dispensing method. The goal is to standardize the number of fries provided. The accompan

> You are considering buying insurance for your new laptop computer, which you have recently bought for $1,500. The insurance premium for three years is $80. Over the three-year period there is an 8% chance that your laptop computer will require work worth

> A consumer advocacy group is concerned about the variability in the cost of a generic drug. There is cause for concern if the variance of the cost exceeds 5 ($)2. The group surveys seven local pharmacies and obtains the following prices (in $) for a part

> 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. a. Construct the 90% interval

> A replacement part for a machine must be produced within close specifications in order for it to be acceptable to customers. A production process is considered to be working properly as long as the variance in the lengths of the parts does not exceed 0.0

> The data accompanying this exercise include monthly rents for a two-bedroom apartment in two campus towns: Ann Arbor, Michigan, and Davis, California. Davis, California, is known to have higher rents than Ann Arbor, Michigan; however, it is not clear if

> A variety of packaging solutions exist for products that must be kept within a specific temperature range. Cold chain distribution is particularly useful in the food and pharmaceutical industries. A packaging company is trying out a new packaging materia

> A portion of the monthly stock prices (rounded to the nearest dollar) for Starbucks Corp. and Panera Bread Co. from 2010 to 2013 are reported in the following table. Source: www.finance.yahoo.com. a. State the null and the alternative hypotheses in or

> A marketing analyst is studying the variability in customer purchase amounts between shopping mall stores and “big box” discount stores. She suspects the variability is different between those stores due to the nature of the customers involved. To invest

> The quality manager at a battery manufacturing company wants to determine if lithium-ion batteries have less variability in discharge time than nickel-cadmium batteries. Using products with similar power draws, he has measured the time until discharge (i

> Nike’s total revenues (in millions of $) for the Asian and Latin American regions for the years 2005 through 2009 are as follows: Source: Nike Online Annual Reports. a. Specify the competing hypotheses in order to test whether the va

> The following table shows the annual returns (in percent) for Fidelity’s Electronic and Utilities funds. Source: www.finance.yahoo.com; data retrieved April 3, 2015. Test if the population variances differ at the 5% significance level

> An appliance store sells additional warranties on its refrigerators. Twenty percent of the buyers buy the limited warranty for $100 and 5% buy the extended warranty for $200. What is the expected revenue for the store from the warranty if it sells 120 re

> Two basketball players on a school team are working hard on consistency of their performance. In particular, they are hoping to bring down the variance of their scores. The coach believes that the players are not equally consistent in their games. Over a

> Consider the following competing hypotheses and relevant summary statistics: Conduct this hypothesis test at the 5% significance level. State your assumptions. (Hint: You may want to first convert the above left-tailed test into a right-tailed test by

> Use the F table to find the value x for which: F table: a. P (F (4,8) ≥ x) = 0.025 b. P (F (4,8) ≥ x) = 0.05 c. P (F (4,8) d. P (F (4,8) dfi df2 Area in Upper Tail, a 6 7 8 0.10 3.05 3.01 2.98 0.05 4.28 4.21 4.15

> 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 to be significant v

> The data accompanying this exercise show miles per gallon (mpg) for 25 cars. State the null and the alternative hypotheses in order to test whether the variance differs from 62 mpg2. a. Assuming that mpg is normally distributed, calculate the value of th

> A realtor in Mission Viejo, California, believes that the standard deviation of house prices is more than 100 units, where each unit equals $1,000. Assume house prices are normally distributed. a. State the null and the alternative hypotheses for the tes

> An economist is interested in the variability of hourly wages at a production plant. She collects data on 50 hourly wage earners. a. Set up the competing hypotheses to test whether the variance of hourly wages exceeds 35 ($2). b. Calculate the value of t

> To maintain high consistency in its manual sewing operations, a custom manufacturer of high-quality fashion clothing has a goal in which all sewing employees should score within a standard deviation of 9 on a sewing dexterity test. To test adherence to t

> Metal works, a supplier of machine parts, fabricates bearings in which the standard deviation of the bearing diameter must be within 0.002-inch maximum. Otherwise, problems with fit will occur. The engineering department is conducting an experiment to in

> Monthly stock prices (in $) for two competing firms are as follows a. Calculate the sample mean, the sample variance, and the sample standard deviation for each firm’s stock price. b. Which firm had the higher average stock price ove

> The India Fund, Inc. (IFN) is a close-ended equity mutual fund launched by the Blackstone Group’s Asset Management arm. Although it promises impressive returns, it does so at the cost of greater risk. An analyst would like to test if th

> A restaurant owner is concerned about the consistency of business. He wants to determine if the standard deviation of the profits for each week is less than $300. The profits from last week are listed below (in dollars). Assume that profits are normally

> The manager of a supermarket would like the variance of the waiting times of the customers not to exceed 3 minutes-squared. She would add a new cash register if the variance exceeds this threshold. She regularly checks the waiting times of the customers

> 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. a. Specify the competing hypotheses that determine whether the sa

> 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 f

> Depression engulfs millions of Americans every day. A federal study reported that 10.9% of adults aged 18–24 identified with some level of depression versus 6.8% of adults aged 65 or older (The Boston Globe, October 18, 2010). Suppose 1,000 young adults

> A Health of Boston report suggests that 14% of 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 hy

> It is important for women to gain the right amount of weight during pregnancy by eating a healthy, balanced diet. It is recommended that a woman of average weight before pregnancy should gain 25 to 35 pounds during pregnancy (www.babycenter.com, August 2

> A farmer is concerned that a change in fertilizer to an organic variant might change his crop yield. He subdivides 6 lots and uses the old fertilizer on one half of each lot and the new fertilizer on the other half. The following table shows the results.

> A study examined “sidewalk rage” in an attempt to find insight into anger’s origins and offer suggestions for anger-management treatments (The Wall Street Journal, February 15, 2011). “Sidewalk ragers” tend to believe that pedestrians should behave in a

> The Federal Reserve Bank of St. Louis is a good source for downloading economic data. Go to research.stlouisfed.org/fred2/ to extract quarterly data on gross private saving (GPSAVE) from 2012 to 2015 (16 observations). Create a table that uses this infor

> It is well documented that cholesterol over 200 is a risk factor in developing heart disease for both men and women (www.livestrong.com, January 11, 2011). Younger men are known to have higher cholesterol levels than younger women; however, beyond age 55

> The accompanying table shows annual return data from 2001–2009 for Vanguard’s Balanced Index and European Stock Index mutual funds. Source: www.finance.yahoo.com a. Set up the hypotheses to test whether the mean ret

> Do men really spend more money on St. Patrick’s Day as compared to women? A survey found that men spend an average of $43.87 while women spend an average of $29.54 (USA Today, March 17, 2009). Assume that these data were based on a sample of 100 men and

> It has generally been believed that it is not feasible for men and women to be just friends (The New York Times, April 12, 2012). Others argue that this belief may not be true anymore since gone are the days when men worked and women stayed at home and t

> A report suggests that business majors spend the least amount of time on course work than all other college students (The New York Times, November 17, 2011). A provost of a university decides to conduct a survey where students are asked if they study har

> Due to late delivery problems with an existing supplier, the director of procurement at Electro Tech began to place orders for electrical switches with a new supplier as part of a “dual-source” (two-supplier) strategy. Now she wants to revert to a “singl

> Only 26% of psychology majors are satisfied with their career paths as compared to 50% of accounting majors (The Wall Street Journal, October 11, 2010). Suppose these results were obtained from a survey of 300 psychology majors and 350 accounting majors.

> According to a report, 32.2% of American adults are obese (The New York Times, August 15, 2008). Among ethnic groups in general, African American women are more overweight than Caucasian women, but African American men are less obese than Caucasian men.

> In an effort to make children’s toys safer and more tamperproof, toy packaging has become cumbersome for parents to remove in many cases. Accordingly, the director of marketing at Toys4Tots, a large toy manufacturer, wants to evaluate the effectiveness o

> There is a declining interest among teenagers to pursue a career in science and health care (U.S. News & World Report, May 23, 2011). Thirty college-bound students in Portland, Oregon, are asked about the field they would like to pursue in college. The c

> The director of housekeeping at Elegante, a luxury resort hotel with two locations (Seaside and Oceanfront), wants to evaluate housekeeping performance at those two locations. Random samples of 100 rooms were inspected at each location for defects (e.g.,

> More people are using social media to network, rather than phone calls or e-mails (U.S. News & World Report, October 20, 2010). From an employment perspective, jobseekers are no longer calling up friends for help with job placement, as they can now get h

> Research by Harvard Medical School experts suggests that boys are more likely than girls to grow out of childhood asthma when they hit their teenage years (BBC News, August 15, 2008). Scientists followed over 1,000 children between the ages of 5 and 12,

> According to the Pew report, 14.6% of newly married couples in 2008 reported that their spouse was of another race or ethnicity (CNN Living, June 7, 2010). In a similar survey in 1980, only 6.8% of newlywed couples reported marrying outside their race or

> Reducing scrap of 4-foot planks of hardwood is an important factor in reducing cost at a wood-flooring manufacturing company. Accordingly, engineers at Lumber works are investigating a potential new cutting method involving lateral sawing that may reduce

> A study claims that girls and boys do not do equally well on math tests taken from the 2nd to 11th grades (Chicago Tribune, July 25, 2008). Suppose in a representative sample, 344 of 430 girls and 369 of 450 boys score at proficient or advanced levels on

> 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 an

> John Daum and Chris Yin are star swimmers at a local college. They are preparing to compete at the NCAA Division II national championship meet, where they both have a good shot at earning a medal in the men’s 100-meter freestyle event. The coach feels th

> The following table presents a portion of the annual returns for Fidelity’s Select Automotive Fund (in percent). This mutual fund invests primarily in companies engaged in the manufacturing, the marketing, or the sales of automobiles, trucks, specialty v

> For staffing purposes, a retail store manager would like to standardize the number of checkout lanes to keep open on a particular shift. She believes that if the standard deviation of the hourly customer arrival rates is 8 customers or less, then a fixed

> The manager of a publishing company plans to give a $20,000 bonus to the top 15%, $10,000 to the next 30%, and $5,000 to the next 10% of sales representatives. If the publishing company has a total of 200 sales representatives, what is the expected bonus

> Fizzco, a beverage manufacturing company, is interested in determining whether the standard deviation of their dispensing process has changed from a required level of 5 milliliters. They have taken a random sample of 12 bottles and have measured the amou

> When faced with a power hitter, many baseball teams utilize a defensive shift. A shift usually involves putting three infielders on one side of second base against pull hitters. Many believe that a power hitter’s batting average is lowe

> It is fairly common for people to put on weight when they quit smoking. While a small weight gain is normal, excessive weight gain can create new health concerns that erode the benefits of not smoking. The accompanying table shows a portion of the weight

> The labor quotation department at Excabar, a large manufacturing company, wants to verify the accuracy of their labor bidding process (estimated cost per unit versus actual cost per unit). They have randomly chosen 35 product quotations that subsequently

> The following table shows the annual returns (in percent) for Fidelity’s Select Electronic and Select Utilities mutual funds for the years 2001 through 2009. Source: www.finance.yahoo.com a. Set up the hypotheses to test the claim tha

> The marketing department at Insure-Me, a large insurance company, wants to advertise that customers can save, on average, more than $100 on their annual automotive insurance policies (relative to their closest competitor) by switching their policies to I

> A report criticizes SAT-test-preparation providers for promising big score gains without any hard data to back up such claims (The Wall Street Journal, May 20, 2009). Suppose eight college-bound students take a mock SAT, complete a three-month test-prep

> A computer technology firm wishes to check whether the speed of a new processor exceeds that of an existing processor when used in one of its popular laptop computer models. Accordingly, it measures the time required (in seconds) to complete seven common

> The quality department at Electro Tech is examining which of two microscope brands (Brand A or Brand B) to purchase. They have hired someone to inspect six circuit boards using both microscopes. Below are the results in terms of the number of defects (e.

> Many attempts have been made to relate happiness with various factors. One such study relates happiness with age and finds that holding everything else constant, people are least happy when they are in their mid-40s (The Economist, December 16, 2010). Da

> 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 examines six properties (in $1,000s) that the apprai

> A diet center claims that it has the most effective weight loss program in the region. Its advertisements say, “Participants in our program lose more than 5 pounds within a month.” Six clients of this program are weigh

> 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 minute

> Consider the following matched-pairs sample that represents observations before and after an experiment. Assume that the sample differences are normally distributed. a. Construct the competing hypotheses to determine if the experiment increases the mag

> Consider the following competing hypotheses and relevant summary statistics: Conduct this test at the 5% significance level. State your assumptions. Hoi oilo s1 Sample 1: s = 935 and n, = 14 Sample 2: s = 812 and n2 = 11

> Consider the following competing hypotheses and relevant summary statistics: Assume that the two populations are normally distributed. Conduct this test at the 5% significance level. Hoi oilo = 1 Hại olo #1 Sample 1: x, = 48.5, s = 18.7, and n, = 1

> Consider the following measures based on independently drawn samples from normally distributed populations: a. Construct the 95% interval estimate for the ratio of the population variances. b. Using the confidence interval from part (a), test if the ra

> A consumer advocacy group is concerned about the variability in the cost of prescription medication. The group surveys eight local pharmacies and obtains the following prices (in $) for a particular brand of medication: a. Calculate the point estimate

> A replacement part for a machine must be produced within close specifications in order for it to be acceptable to customers. A random sample of 20 parts drawn from a normally distributed population yields a sample variance of s2 = 0.03. a. Construct the

> Researchers at the Wharton School of Business have found that men and women shop for different reasons. 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, they make big pu

> Access the data accompanying this exercise. a. Compute and interpret the correlation coefficient for household income and house value. b. Compute and interpret the correlation coefficient for household income and the percentage of the residents who are

> Recent evidence suggests that graduating from college during bad economic times can impact the graduate’s earning power for a long time (Financial Times, June 1, 2012). An associate dean at a prestigious college wants to determine if the starting salary

> Baseball has always been a favorite pastime in America and is rife with statistics and theories. In a paper, researchers showed that major league players who have nicknames live an average of 2½ years longer than those without them (The Wall Street Journ