Vitamin D is essential for strong, healthy bones. Although the bone disease rickets was largely eliminated in England during the 1950s, some people there are concerned that this generation of children is at increased risk because they are more likely to watch TV or play computer games than spend time outdoors. Recent research indicated that about 20% of British children are deficient in vitamin D. A company that sells vitamin D supplements tests 320 elementary school children in one area of the country. Use a Normal approximation to find the probability that no more than 50 of them have vitamin D deficiency.
> For each description of data in Exercises 7 to 26, identify the W’s, name the variables, specify for each variable whether its use indicates it should be treated as categorical or quantitative, and for any quantitative variable identify the units in whic
> For each description of data in Exercises 7 to 26, identify the W’s, name the variables, specify for each variable whether its use indicates it should be treated as categorical or quantitative, and for any quantitative variable identify the units in whic
> For each description of data in Exercises 7 to 26, identify the W’s, name the variables, specify for each variable whether its use indicates it should be treated as categorical or quantitative, and for any quantitative variable identify the units in whic
> For each description of data in Exercises 7 to 26, identify the W’s, name the variables, specify for each variable whether its use indicates it should be treated as categorical or quantitative, and for any quantitative variable identify the units in whic
> Develop your own table of data that is a business example of Simpson’s Paradox. Explain the conflict between the conclusions made from the conditional and marginal distributions.
> A 1975 article in the magazine Science examined the graduate admissions process at Berkeley for evidence of gender bias. The following table shows the number of applicants accepted to each of four graduate programs. a) What percent of total applicants
> Researchers testing a new medication find that 7% of users have side effects. To how many patients would a doctor expect to prescribe the medication before finding the first one who has side effects?
> A company must decide which of two delivery services they will contract with. During a recent trial period, they shipped numerous packages with each service and have kept track of how often deliveries did not arrive on time. Here are the data. a) Compa
> An insurance company that provides medical insurance is concerned with recent data. They suspect that patients who undergo surgery at large hospitals have their discharges delayed for various reasons— which results in increased medical
> A company that distributes a variety of pet foods is planning their next advertising campaign. Since different publications are read by different market segments, they would like to know how pet ownership is distributed across different income segments.
> Look back at the table in Exercise 43 concerning desires for success and a high-paying career. That table presented only the percentages, but Pew Research reported the numbers of respondents in the major categories: With this additional information you
> A department store is planning its next advertising campaign. Since different publication are read by different market segments, they would like to know if they should be targeting specific age segments. The results of a marketing survey are summarized i
> The Motion Picture Association of America studies the ethnicity of moviegoers to understand changes in the demographics of moviegoers over time. Here are the numbers of moviegoers (in millions) classified as to whether they were Hispanic, African- Americ
> The U.S. Department of Labor (www.bls.gov) collects data on the number of U.S. workers who are employed at or below the minimum wage. Here is a table showing the number of hourly workers by Age and Sex and the number who were paid at or below the prevail
> Pew research surveyed 25- to 34-yearold adults in 2013 and asked them how important it is “to you personally” to have a high-paying job? Here is a table reporting the responses. a) What percent of women consider it v
> In 2015, the following data were reported by the U.S. Census Bureau. The data show the number of people (in thousands) living above and below the poverty line in each of the four regions of the United States (www.census.gov/content/dam/Census/ library/pu
> A study by the University of Texas Southwestern Medical Center examined 626 people to see if there was an increased risk of contracting hepatitis C associated with having a tattoo. If the subject had a tattoo, researchers asked whether it had been done i
> Suppose a computer chip manufacturer rejects 2% of the chips produced because they fail presale testing. Assuming the bad chips are independent, find the probability of each of the following. a) The fifth chip they test is the first bad one they find.
> The following table shows attendance data collected by the Motion Picture Association of America during the period 2014 to 2016. Figures are the number (in millions) of frequent moviegoers in each age group. a) What percent of all frequent moviegoers o
> The following table shows the number of films in each MPAA (www.mpaa.org) rating by year for each of the years between 2006 and 2015. (Data extracted from Movies 06-15) a) What percent of all these films are G rated? b) What percent of all films in 200
> The same university as in Exercise 37 reported the following data on the gender of their students in their two MBA programs. a) What percent of all MBA students are women? b) What percent of Two-Year MBAs are women? c) What percent of Evening MBAs are
> A survey of the entering MBA students at a university in the United States classified the country of origin of the students, as seen in the table. a) What percent of all MBA students were from North America? b) What percent of the Two-Year MBAs were fr
> It has become more common for shoppers to “comparison shop” using the Internet. Respondents to a Pew survey who owned cell phones were asked whether they had, in the past 30 days, looked up the price of a product while
> The movie ratings system is a voluntary system operated jointly by the Motion Picture Association of America (MPAA) and the National Association of Theatre Owners (NATO). The ratings themselves are given by a board of parents who are members of the Class
> Apple, Inc., divides their expenses into four categories: Cost of Revenue; Research & Development; Selling, General, & Administrative; and Income Taxes. The table below shows these categories for Apple from 2014 to 2016. a) What percent of tota
> The government and many companies are interested in the number of people who lose their home because they are unable to pay. The process of losing a home has three stages, which begin with a “foreclosure filing.” At so
> A company started and managed by business students is selling campus calendars. The students have conducted a market survey with the various campus constituents to determine sales potential and identify which market segments should be targeted. (Should t
> The following table displays information for 470 of the S&P 500 stocks, on how their one-day change on a day on which the S&P 500 index gained 1.23% compared with their year-to-date change. a) What percent of the companies reported a positive c
> A salesman normally makes a sale (closes) on 80% of his presentations. Assuming the presentations are independent, find the probability of each of the following. a) He fails to close for the first time on his fifth attempt. b) He closes his first prese
> A study of a sample of 1057 houses in upstate New York reports the following percentages of houses falling into different Price and Size categories. a) Are these column, row, or total percentages? How do you know? b) What percent of the highest priced
> GE derives revenue from eight operating segments, including three iconic divisions: Power, Aviation, and Healthcare. The following table shows the percentage of all revenue derived from these sources for the period from 2011 to 2015. a) Are these row o
> Here are the same data you saw in Exercise 77 after re-expressions as the square root of assets and the logarithm of assets. a) Which re-expression do you prefer? Why? b) In the square root re-expression, what does the value 50 actually indicate about
> Here is a histogram of the assets (in millions of dollars) of 79 companies chosen from the Forbes list of the nation’s top corporations. a) What aspect of this distribution makes it difficult to summarize, or to discuss, center and sp
> Here is a histogram of the monthly CPI as reported by the Bureau of Labor Statistics (www.bls.gov/cpi) from January 2007 through August 2017. Here is the time series plot for the same data. a) What features of the data can you see in the histogram th
> The histogram shows the monthly U.S. unemployment rate from January 2003 to August 2017. Here is the time series plot for the same data. a) What features of the data can you see in the histogram that aren’t clear in the time series
> Standard and Poor’s Case- Shiller Home Price Index measures the residential housing market in metropolitan regions across the United States. The national index, Composite.10, is a composite of 10 regions, and can be found in the data set provided for the
> The data set provided contains U.S. regular retail gasoline prices (cents/gallon) from 2007 to August 2017, from a national sample of gasoline stations obtained from the U.S. Department of Energy. a) Create a histogram of the data and describe the distri
> The World Bank, through their Doing Business project (www.doingbusiness.org), ranks nearly 200 economies on the ease of doing business. One of their rankings measures the ease of starting a business and is made up (in part) of the following variables: nu
> FAOSTAT, the Food and Agriculture Organization of the United Nations, collects information on the production and consumption of more than 200 food and agricultural products for 200 countries around the world. Here are two tables, one for meat consumption
> Can we use probability models based on Bernoulli trials to investigate the following situations? Explain. a) You survey 500 potential customers to determine their color preference. b) A manufacturer recalls a doll because about 3% have buttons that are
> Here are the number of domestic f lights flown in each year from 2000 to 2016 (www.transtats.bts.gov/homepage.asp): a) Find the correlation of Flights with Year. b) Make a scatterplot and describe the trend. c) Why is the correlation you found in part
> Laptop computers have been growing in popularity according to a study by Current Analysis Inc. Laptops now represent more than half the computer sales in the United States. A campus bookstore sells both types of computers and in the last semester sold 56
> The CEO of a mid-sized company has to relocate to another part of the country. To make it easier, the company has hired a relocation agency to help purchase a house. The CEO has 5 children and so has specified that the house have at least 5 bedrooms, but
> A business student is searching for a used car to purchase, so she posts an ad to a website saying she wants to buy a used Jeep between $18,000 and $20,000. From Kelley’s BlueBook.com, she learns that there are 149 cars matching that de
> A cell phone manufacturer samples cell phones from the assembly to test. She noticed that the number of faulty cell phones in a production run of cell phones is usually small and that the quality of one day’s run seems to have no bearing on the next day.
> A website manager has noticed that during the evening hours, about 3 people per minute check out from their shopping cart and make an online purchase. She believes that each purchase is independent of the others. a) What model might you suggest to model
> My employee seems to leave work anytime between 5 pm and 6 pm, uniformly. a) What is the probability he will still be at work at 5:45 pm? b) What is the probability he will still be at work at 5:45 pm every day this week (M–F)? c) What did you assume
> Defects can occur anywhere on the wheel of a car during the manufacturing process. If X is the angle where the defect occurs, measured from a reference line, then X can be modeled as a uniform random variable on the interval from 0 to 360 degrees. a) Wh
> A tennis player has taken a special course to improve her serving. She thinks that individual serves are independent of each other. She has been able to make a successful first serve 70% of the time. Use a Normal approximation to find the probability she
> Can we use probability models based on Bernoulli trials to investigate the following situations? Explain. a) Each week a doctor rolls a single die to determine which of his six office staff members gets the preferred parking space. b) A medical researc
> Police estimate that 80% of drivers wear their seatbelts. They set up a safety roadblock, stopping cars to check for seatbelt use. If they stop 120 cars, what’s the probability they find at least 20 drivers not wearing their seatbelt? Use a Normal approx
> A lecture hall has 200 seats with folding arm tablets, 30 of which are designed for left-handers. The typical size of classes that meet there is 188, and we can assume that about 13% of students are left-handed. Use a Normal approximation to find the pro
> The Atlas BodyBuilding Company (ABC) sells “starter sets” of barbells that consist of one bar, two 20-pound weights, and four 5-pound weights. The bars weigh an average of 10 pounds with a standard deviation of 0.25 pound. The weights average the specifi
> At a certain coffee shop, all the customers buy a cup of coffee; some also buy a doughnut. The shop owner believes that the number of cups he sells each day is normally distributed with a mean of 320 cups and a standard deviation of 20 cups. He also beli
> The bicycle shop in Exercise 55 estimates using current labor costs that unpacking a bike costs $0.82 on average with a standard deviation of $0.16. Assembly costs $8.00 on average with a standard deviation of $0.88 and tuning costs $4.10 with a standard
> Bicycles arrive at a bike shop in boxes. Before they can be sold, they must be unpacked, assembled, and tuned (lubricated, adjusted, etc.). Based on past experience, the shop manager makes the following assumptions about how long this may take: â&#
> You’re thinking about getting two dogs and a cat. Assume that annual veterinary expenses are independent and have a Normal model with the means and standard deviations described in Exercise 52. a) Define appropriate variables and express the total annua
> In Exercise 51 we poured a large and a small bowl of cereal from a box. Suppose the amount of cereal that the manufacturer puts in the boxes is a random variable with mean 16.2 ounces and standard deviation 0.1 ounce. a) Find the expected amount of cere
> Consider each of these situations. Do you think the proposed sampling method is appropriate? Explain. a) We want to know if business leaders in the community support the development of an “incubator” site at a vacant lot on the edge of town. We spend a d
> Consider each of these situations. Do you think the proposed sampling method is appropriate? Explain. a) We want to know what percentage of local doctors accept Medicaid patients. We call the offices of 50 doctors randomly selected from local Yellow Page
> A real-estate broker in Washington, DC, purchased 3 two-bedroom houses in a depressed market for a combined cost of $1,000,000. He expects the cleaning and repair costs on each house to average $100,000 with a standard deviation of $15,000. When he sells
> For the investment experiment of Exercise 2, identify how Control, Randomization, and Replication were used. Exercise 2: For the following experiment, identify the experimental units, the treatments, the response, and the random assignment. An investme
> Concerned about reports of discolored scales on fish caught downstream from a newly sited chemical plant, scientists set up a field station in a shoreline public park. For one week they asked fishermen there to bring any fish they caught to the field sta
> Sammy’s Salsa, a small local company, produces 20 cases of salsa a day. Each case contains 12 jars and is imprinted with a code indicating the date and batch number. To help maintain consistency, at the end of each day, Sammy selects three bottles of sal
> A manufacturing company employs 14 project managers, 48 foremen, and 377 laborers. In an effort to keep informed about any possible sources of employee discontent, management wants to conduct job satisfaction interviews with a simple random sample of emp
> A consumer group wants to test the effectiveness of a new “organic” laundry detergent and make recommendations to customers about how to best use the product. They intentionally stain 30 white T-shirts with grass in order to see how well the detergent wi
> An industrial machine requires an emergency shutoff switch that must be designed so that it can be easily operated with either hand. Design an experiment to find out whether workers will be able to deactivate the machine as quickly with their left hands
> Can special study courses actually help raise SAT scores? One organization says that the 30 students they tutored achieved an average gain of 60 points when they retook the test. a) Explain why this does not necessarily prove that the special course caus
> Hoping to learn how to control crop damage by a certain species of beetle, a researcher plans to test two different pesticides in small plots of corn. A few days after application of the chemicals, he’ll check the number of beetle larvae found on each pl
> A research doctor has discovered a new ointment that she believes will be more effective than the current medication in the treatment of shingles (a painful skin rash). Eight patients have volunteered to participate in the initial trials of this ointment
> A study published in the New England Journal of Medicine (Aug. 2001) suggests that it’s dangerous to enter a hospital on a weekend. During a 10-year period, researchers tracked over 4 million emergency admissions to hospitals in Ontario, Canada. Their fi
> Do cars get better gas mileage with premium instead of regular unleaded gasoline? It might be possible to test some engines in a laboratory, but we’d rather use real cars and real drivers in real day-to-day driving, so we get 20 volunteers. Design the ex
> A collector purchased a quantity of action figures and is going to sell them on eBay. He has 19 Hulk figures. In recent auctions, the mean selling price of similar figures has been $12.11, with a standard deviation of $1.38. He also has 13 Iron Man figur
> Some schools teach reading using phonics (the sounds made by letters) and others using whole language (word recognition). Suppose a school district wants to know which method works better. Suggest a design for an appropriate experiment.
> A medical researcher suspects that giving post-surgical patients large doses of vitamin E will speed their recovery times by helping their incisions heal more quickly. Design an experiment to test this conjecture. Be sure to identify the factors, levels,
> Before drilling for water, many rural homeowners hire a dowser (a person who claims to be able to sense the presence of underground water using a forked stick). Suppose we wish to set up an experiment to test one dowser’s ability. We get 20 identical con
> Giant food stores serves two customer segments: “Budget Shoppers” and “Foodies.” Giant sends 1000 of each type of customer one of two circulars: Deep Discounts or Gourmet Food. The r
> Verizon Wireless wants to test new package deals. They are considering offering three levels of data per month (5 Gb, 10 Gb, Unlimited) and two different international calling options (no international calling, discounted international). They randomly as
> Kraft foods wants to see whether a coupon will affect sales for macaroni and cheese. Kraft picks a single grocery store in Philadelphia in which to test two coupon types: “buy one, get one free” and “
> A small maker of video games designs a pricing experiment. They know that some teens self-identify as “gamers,” while others do not. They market a new video game to gamers and non-gamers, and they send half of each gro
> Recently, a group of adults who swim regularly for exercise were evaluated for depression. It turned out that these swimmers were less likely to be depressed than the general population. The researchers said the difference was statistically significant.
> A Danish study published in the Archives of Internal Medicine casts significant doubt on suggestions that adults who drink wine have higher levels of “good” cholesterol and fewer heart attacks. These researchers followed a group of individuals born at a
> Contrast bath treatments use the immersion of an injured limb alternately in water of two contrasting temperatures. Those who use the method claim that it can reduce swelling. Researchers compared three treatments: (1) contrast baths and exercise, (2)
> An option to buy a stock is priced at $200. If the stock closes above 30 on May 15, the option will be worth $1000. If it closes below 20, the option will be worth nothing, and if it closes between 20 and 30 (inclusively), the option will be worth $200.
> An experiment showed that subjects fed the DASH diet were able to lower their blood pressure by an average of 6.7 points compared to a group fed a “control diet.” All meals were prepared by dietitians. a) Why were the subjects randomly assigned to the d
> The analyst who designed the experiment in Exercise 28 obtained the data, which is plotted are in the graph below. a) Is there an interaction effect that is large enough to be worrisome? b) The regional manager of the chain is having trouble interpreti
> A supermarket wants to see the effects of coupons on spending. They believe that male and female heads of households will respond differently to the coupons. The supermarket chooses 200 males and 200 females, and sends half of each group the coupon, whil
> A humor piece published in the British Medical Journal (“Parachute Use to Prevent Death and Major Trauma Related to Gravitational Challenge: Systematic Review of Randomized Control Trials,” Gordon, Smith, and Pell, BMJ, 2003:327) notes that we can’t tell
> A swimsuit manufacturer wants to test the speed of its newly designed suit. The company designs an experiment by having 6 randomly selected Olympic swimmers swim as fast as they can with their old swimsuit first and then swim the same event again with th
> A running-shoe manufacturer wants to test the effect of its new sprinting shoe on 100-meter dash times. The company sponsors 5 athletes who are running the 100-meter dash in the 2012 Summer Olympic games. To test the shoe, it has all 5 runners run the 10
> The boxplots display case prices (in dollars) of wine produced by wineries along three of the Finger Lakes in upstate New York. a) Is this an experiment? Explain. b) Does there seem to be evidence that prices may differ by location? Explain. 150 1
> These boxplots show the relationship between the number of cylinders in a car’s engine and its fuel economy from a study conducted by a major car manufacturer. a) Is this an experiment? Explain. b) Do the boxplots indicate that cars w
> An industrial machine requires an emergency shutoff switch that must be designed so that it can be easily operated with either hand. Design an experiment to find out whether workers will be able to deactivate the machine as quickly with their left hands
> Can special study courses actually help raise SAT scores? One organization says that the 30 students they tutored achieved an average gain of 60 points when they retook the test. a) Explain why this does not necessarily prove that the special course cau
> Mary is deciding whether to book the cheaper f light home college after her final exams, but she’s unsure when her last exam will be. She thinks there is only a 20% chance that the exam will be scheduled after the last day she can get a seat on the cheap
> A Danish study published in the Archives of Internal Medicine casts significant doubt on suggestions that adults who drink wine have higher levels of “good” cholesterol and fewer heart attacks. These researchers followed a group of individuals born at a
> The makers of Frumpies, “the breakfast of rug rats,” want to improve their marketing, so they consult you. a) They first want to know what fraction of children, ages 10 to 13, like their celery-flavored cereal. What kind of study should they perform? b
> An advertisement selling specially designed CDs of Mozart’s music specifically because they will “strengthen your mind, heal your body, and unlock your creative spirit” claims that “in Japan, a brewery actually reported that their best sake is made when
> Will listening to a Mozart piano sonata make you smarter? In a published study, Rauscher, Shaw, and Ky reported that when students were given a spatial reasoning section of a standard IQ test, those who listened to Mozart for 10 minutes improved their sc
> A swimsuit manufacturer wants to test the speed of its newly designed $550 suit. They design an experiment by having 6 randomly selected Olympic swimmers swim as fast as they can with their old swimsuit first and then swim the same event again with the n
