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Business Statistics 3rd Edition Robert A. Donnelly - Solutions
Many of my students over the last couple of years have been earning money as Instagram influencers. The amount of influencers and their popularity has been growing steadily. The top 50 Instagram influencers (www.influencermarkinghub.com) have over 3 billion followers together. Unfortunately, this
The Twin Cities Pioneer Press argued in a 2018 article that wine and cheese were important for world history and the development of human physiology. A researcher was interested in studying if there is actually a strong positive relationship between wine and cheese consumption. The following table
EcoSmart is a manufacturer of compact fluorescent light (CFL) bulbs, which are fluorescent bulbs designed to be more efficient than traditional incandescent bulbs. In an effort to produce a consistent product, suppose EcoSmart has a goal that the standard deviation for the life of its CFL bulbs is
A 2018 paper by the National Bureau for Economic Research (NBER Working Paper No. 24639) showed that heat exposure inhibits cognitive skill development. Using results from 10 million PSAT exams, researchers showed that without air conditioning, each 1°F increase in school year temperature reduces
A recent poll by the Web page weloveanycar.com asked respondents, ?Would you consider buying a totally electric car with a range of 300 miles to one charge?? The results are shown in the following table. Suppose Mercedes would like to confirm these results with its own survey, so the company asked
To make predictions about financial markets it is important to determine the distributional form of average daily returns. Of course, in practice you should use as much data as possible to make this decision. Here we will use daily returns for 128 days of trading of May 1, 2017, to October 30,
Data from the UEFA , Union of European Football Associations, shows that during the 2000, 2004, 2008, 2012, and 2016 knockout stages of the European Championships in soccer a total of 104 penalty shots were taken during penalty shootouts. The following figure shows the data for the placements of
The following table shows the distribution of the ages of Snapchat users in December 2016 (statista.com). The table also shows the observed frequencies from a random sample of Snapchat users for 2018. a. Using ? = 0.05, perform a chi-square test to determine if the ages of Snapchat users changed
The following table shows the U.S. market share for smartphone manufacturers in 2017 according to the research firm comScore. The table also shows the frequency of purchases of smartphones by brand for a random sample of customers during 2018. a. Using ? = 0.05, perform a chi-square test to
The following table shows the medal count for the top three countries at the 2018 Winter Olympics. a. Using ? = 0.05, perform a chi-square test to determine if the type of medal and country that earned it are independent of one another. b. What conclusions can be made based on these results? c.
The following table shows the U.S. market share for automotive manufacturers in 2013. Also shown is the frequency of car purchases by manufacturer from a random sample of 220 customers in March of 2018 (www.motorintelligence.com). a. Using ? = 0.10, perform a chi-square test to determine if the
In 1991 the Consumer Bankruptcy Project conducted a study to determine the education levels of people who declare bankruptcy. The percentages are shown in the following table. Also shown in the table is the observed frequency for these education levels from a random sample of individuals who filed
According to a recent AAA survey, about 20% of Americans say they?re likely to buy an electric car in the future. Actually, sales of electric cars increased by 25% between 2016 and 2017. To serve U.S. customers, Consumer Research is currently testing the new Nissan Leaf, Tesla Model 3, and Chevy
Suppose you are interested in buying a new smart TV and want to find out about differences in prices, sizes, and manufacturers. The following data show the prices of a random sample of televisions for various screen sizes. These data can also be found in the Excel file Consumer Reports.xlsx. a.
Happiness Works (https://friday.work), a consulting group dedicated to improving work conditions, recently showed that 18- to 34-year-olds are the happiest workers in the U.S. economy. They showed that only 8% of workers 18 to 34 years old stated that they are unhappy, whereas 16% of workers 35 to
According to Forbes, pickled foods are one of the big food trends of 2018. In fact, pickled foods have become so popular that even KFC and food stands in baseball stadiums started to offer pickled food. I am not sure that pickled foods are really as popular as Forbes wants us to believe and asked
Fitness trackers are nearly ubiquitous these days. I asked three randomly selected students to report heir minutes of physical activity per week for the last several weeks. These data can also be found in the Excel file minutes.xlsx. a. Perform a one-way ANOVA using ? = 0.05 to determine if there
Many students regularly complain that the cost of college textbooks is constantly increasing. However, the National Association of College Stores released data for 2016 and 2017 for the average amount of money spent on course materials, which shows that the average in 2016 was $327 and in 2017
A 2017 survey found that the daily time spent on social media differs by age group. You select random samples of people from each age group to verify the information. The following table lists the difference of time spent by the groups 16- to 24-year-olds and 25- to 34-year-olds from your
During the 2007–2008 decline in the housing market, it appeared that the average size of a newly constructed house fell. To investigate this trend, the square footages of a random sample of houses built in 2008 were compared to houses built in 2018. A random sample of 45 homes built in 2008 had a
Walmart has an interest in monitoring the average back-to-school spending for grade-school students year to year. Every year the back-to-school spending data is published by the National Retail Federation (nrf.com). The following table shows the average backto-school spending of households randomly
A constant question for social media is if it is a profitable business. A key determinant of profit is the average revenue per user (ARPU). Social media platforms like Facebook and Snapchat usually report their ARPU in their quarterly earnings statements. The worldwide ARPU for Snapchat in the
Small businesses (See Problem 9.63) are viewed by many as the backbone of the U.S. economy. Smallbusiness owners are often described as entrepreneurs, requiring a variety of skills in order to be successful. A 2016 survey of small-business owners found that 47% had a college degree beyond a
Small businesses are viewed by many as the backbone of the U.S. economy. Small-business owners are often described as entrepreneurs, requiring a variety of skills in order to be successful. According to the 2016 Babson College’s State of Small Business study, the average small business owner is a
According to the U.S. Department of Labor, 10.7% of the U.S. workforce was unionized in 2017. This percentage has declined steadily since the end of World War II, when more than a third of U.S. workers belonged to a union. Suppose the department would like to test the hypothesis that the proportion
The average wait time on the phone for taxpayers calling the IRS in 2015 was 1,380 seconds. Suppose (if you can use your imagination) that the IRS made operational changes in an effort to reduce wait times. To test the effectiveness of these changes, a random sample of 50 phone calls was selected
During 2016, the average monthly bill for digital cable in the United States was $103 according to research firm Centris. Suppose Comcast would like to test the hypothesis that the average monthly bill is higher than $103 this year. A random sample of 52 households was chosen. Assume the standard
According to Pew Research Center’s data from 2016, 7% of Americans are classified as “super users” of shared and on-demand services, such as ordering groceries online, contributing to online fundraising, and using ride-hailing apps. A superuser is classified as somebody who has used more than
According to the 2017 Survey of Physician Appointment Wait Time, patients had to wait an average of 24 days to schedule a new appointment with a doctor. A random sample of 40 patients in 2018 was selected and the number of days they had to wait to schedule an appointment was recorded. These data
The amount of text messages sent in the United States has been steadily declining since its peak in 2011 with 2,304 billion messages sent per year, which is about 960 text messages per month per cell phone owner. This number declined steadily to reach 592 text messages per month per cell phone
According to Pew Research Center surveys, 8% of American adults did not own a cell phone in 2015. Suppose Verizon Wireless would like to test if this percentage has recently changed. A recent random sample of 280 American adults was selected, and it was found that 16 of them did not own a cell
According to 2016 data from the U.S. Census Bureau, only 32% of Americans are saving for retirement in a 401(k). A random sample of 340 Americans was recently selected, and it was found that 119 of them made contributions to their 401(k) plans this year.a. Using α = 0.01, perform a hypothesis test
Smart meters are a special type of electrical meter that monitors the usage of electricity and communicates that information back to the utility company. According to a report by the Energy Information Administration from December 2017, 47% of homes in the United States were equipped with smart
According to Fidelity Investments, the average 401(k) account balance was $99,900 in 2017. To test if this average has recently changed, suppose a sample of 30 401(k) plans was recently selected, and it was found that the average 401(k) balance was $110,110. Assume the population standard deviation
In May 2018, the Web site NBAstuffer.com reported that 18 of the 30 NBA teams have 3 or more employees whose sole responsibility is to analyze data. The information compiled by these “statheads” is then used to help make decisions about player development and roster construction, game-planning
A 2015 survey by the American Marketing Association showed that 47% of Snapchat users are between 18 and 24 years old. Suppose a follow-up survey were recently conducted to investigate if the proportion had changed and that out of a random sample of 225 Snapchat users, it found that 126 users were
According to the Glassdoor.com, each job opening on average attracted 250 résumés in 2016. You know that the job market improved in 2017 compared to 2016, which means that more people will likely be switching jobs but also fewer unemployed workers remain in the labor market. To find out which
A Gallup poll from 2016 showed that the share of Americans who are “extremely proud” to be American has been steadily decreasing since 2000 to 52% in 2016. Suppose the White House staff is concerned that the rating has fallen further. Let’s say that out of a random sample of 300 adults, 144
According to a 2016 report by Fannie Mae, 39% of 18-to 20-year-old students use credit cards for everyday purchases. Suppose a local bank believes that this share will increase over time because of shopping behaviors of students. To test this hypothesis, a random sample of 275 students was
According to statista.com, the average room rate for a New York City hotel in 2016 was $337. Suppose the Chamber of Commerce of New York City would like to test if this rate has changed recently by randomly sampling 40 room rates. The mean of this sample was found to be $351.20. Assume the
According to Pew Research, 21% of people who use online dating services are 35 to 44 years old. There is also information that this percentage has steadily increased over the previous years. Assume Pew recently sampled 125 households randomly to test the hypothesis that the proportion of people
The average retirement age for French citizens between 2011 and 2016 was reported to be 59.7 years according to the Organization for Economic Cooperation and Development, an international group dedicated to promoting trade and economic growth. With the French pension system operating with a
The number of long-term unemployed, defined as those out of work for more than 27 weeks, has been a detriment to the recent economic recovery. At its peak after the most recent recession, that rate reached 45.1% in July 2011 but has been steadily declining since then to 20% in April 2018.
The Majoring in Money study by Sallie Mae from December 2015 showed that most college students manage their credit cards in a reasonable way. It showed that almost two-thirds of students pay their credit card balance in full every month and 26% of students who own credit cards make partial payments
A recent survey by Statistic Brain showed that 64% of users of online dating sites say the number one thing they’re looking for in a date or partner is common interests. Suppose you would like to perform a hypothesis test to challenge this finding. From a random sample of 170 students on campus,
Consumers with credit scores below 600 have a very difficult time getting approved for car or mortgage loans. In 2017, 30% of Americans had a credit score below 600. The Federal Reserve Bank of New York regularly monitors credit scores to judge the health of the U.S. economy. Because household debt
An increased number of U.S. colleges have been using online resources such as Facebook and Google to research applicants. According to Kaplan Test Prep, 35% of admissions officers indicated that they visited an applying student’s social networking page in 2017. A random sample of 100 admissions
Fannie Mae is a government-sponsored organization that was established in 1938 after the Depression to provide local banks with money from the federal government to be used for residential mortgages in an effort to increase home-ownership rates. As lending standards have tightened during the most
According to the financial reports by Snapchat, the average daily user of Snapchat created 19 messages, or ?snaps,? per day in Q3 2017. You want to find out if the number of Snapchat messages has changed since Q3 2017 and create a random sample using information from students on your campus for the
According to National Retail Foundation, holiday shoppers spent an average of $935.58 over the Thanksgiving weekend in 2016. The following data show the amount spent by a random sample of holiday shoppers during the same weekend in 2017: a. Test the hypothesis that that shoppers spent less than
Suppose the average size of a new house built in a certain county in 2014 was 2,272 square feet. A random sample of 25 new homes built in this county was selected in 2018. The average square footage was 2,190, with a sample standard deviation of 225 square feet. a. Using α = 0.02, does this sample
According to the 2016 Majoring in Money report bythe government-lending institution Sallie Mae, 18-to 20-year-old college students have an averagecredit card balance of $569. You want to find out ifthis number is lower now and collect data for a randomsample of 40 college students. Their
Determine the critical t-scores for each of the following conditions:a. One-tail test, α = 0.05, and n = 21b. Two-tail test, α = 0.02, and n = 10c. Two-tail test, α = 0.05, and n = 28d. Two-tail test, α = 0.01, and n = 40
According to the “Majoring in Money” 2016 report by the government-lending institution Sallie Mae, college students who have credit cards have an average credit card balance of $1,076. A random sample of 50 college students was selected, and their average credit card debt was found to be
Recently released data by the American Pet Products Association showed that in 2016 the majority (38%) of dog owners were part of Generation Y (born 1994–1980). You want to open a cage-free dog salon and in order to plan your marketing strategy for the salon, you would like to estimate the
The Board of Governors of the U.S. Federal Reserve System regularly monitors credit card delinquency rates in the United States. At its peak after the 2007–2008 recession, delinquency rates reached 6.77% in the second quarter of 2009. Since its peak, delinquency rates have declined to a new low
According to recent data by the American Marketing Association, 78.6% of people in the 18–24 age group used Snapchat in 2017. You want to find out what the Snapchat penetration is among your classmates who are all between 18 and 24 years old. Suppose you obtain a random sample of 260 students and
According to data from the Board of Governors of the Federal Reserve System, student loan debt reach $1.5 trillion in the first quarter of 2018. However, you also know from the research of economist Susan Dynarski from the University of Michigan that the majority of students actually do not borrow
Because of the multitude of positive health benefits for infants and mothers, one provision of the Affordable Care Act, commonly known as Obamacare, requires that insurance plans pay forbreast-feeding support for mothers, such as consultations and breast pumps. According to the Centers for Disease
In 2017 the German Soccer Bundesliga introduced a video to review certain critical plays. However, the system has not been without its controversies. On April 16, 2018 the referee of the game Mainz against Freiburg waved away appeals from the home side for handball in the penalty area, then
According to the Bureau of Labor Statistics, the average hourly wage in the United States was $26.84 in April 2018. To confirm this wage, a random sample of 36 hourly workers was selected during the month. The average wage for this sample was $25.35. Assume the standard deviation of wages for the
According to the Centers for Disease Control and Prevention, 15.5% of the U.S. population smoked in 2016. In 2018, a random sample of 650 Americans was selected, 79 of whom smoked.a. Construct a 90% confidence interval to estimate the actual proportion of people who smoked in the United States in
Although Germany has one of the healthiest economies in the euro zone, it has one of the lowest homeownership rates in Europe, and the homeownership rates in Germany have been declining since 2012. According to Eurostat, the German homeownership rate was 51.7% in 2017 (compared to 63.9% in the
The percentage of high school graduates applying to multiple colleges has been increasing over the past several years. According to the National Association for College Admission Counseling, 36% of high school students applied to seven or more colleges in 2015. A random sample of 350 high school
The IRS reported that 90% of individual tax returns were filed electronically in 2017. A random sample of 225 tax returns from 2018 was selected. From this sample, 197 were filed electronically.a. Construct a 95% confidence interval to estimate the actual proportion of taxpayers who filed
The U.S. Department of Education reported that in 2015, 69.2% of students enrolled in college or a trade school within 12 months of graduating from high school. In 2017, a random sample of 160 individuals who graduated from high school 12 months prior was selected. From this sample, 102 students
The American Automobile Association (AAA) reported that the national average price of regular gasoline on May 17, 2018 was $2.90 per gallon. The following data show the price per gallon of regular gasoline for 15 randomly selected stations in your area. These data can also be found in the Excel
According to statista.com, workers in Brazil lead the world in paid vacation days, averaging 41 days per year. The following data show the number of paid vacation days for a random sample of 20 Brazilian workers. These data can also be found in the Excel file titled paid vacation.xlsx.48 40 30 58
According to Autolist.com, the most popular car for millennials is the Honda Civic. However, according to JDPower.com, the average age of a Civic driver is actually 50. Suppose you draw a random sample of 18 Civic drivers and find the average age of the drivers to be 52.5 years. Assume the standard
The cost of ink cartridges for inkjet printers can be substantial over the life of a printer. Printer manufacturers publish the number of pages that can be printed from an ink cartridge in an effort to attract customers. HP claims that the CN045W black print cartridge (the most popular black ink
The average selling price of an iPhone purchased by a random sample of 35 customers was $796. Assume the population standard deviation was $90.a. Construct a 90% confidence interval to estimate the average selling price in the population with this sample.b. What is the margin of error for this
In January of 2018 Bank of America started charging customers a $12 checking account fee. Of course, customers were upset with this change. However, Bank of America claimed that their checking account fees are some of the lowest in the industry. You decide to check Bank of America’s claim and
According to Catalyst, 26.5% executive positions in Fortune 500 companies are occupied by women in 2016. A random sample of 180 Fortune 500 executives was selected.a. What is the probability that 30% or less of this sample were women?b. What is the probability that 25% or more of this sample were
In 2016 Americans owed $1.3 trillion in student loans. The default rates of college student loans determine eligibility for colleges to receive federal student aid. According to the Department of Education, an average of 11.5% of Americans who had student loans defaulted on their loans. A random
According to the Graduate Management Admission Council, the average starting salary for an MBA graduate in the class of 2016 was $105,000. Assume the population standard deviation for starting MBA salaries was $15,000. A random sample of 40 MBA graduates from the class of 2016 was selected.a. What
As of March 2018, 52 companies have been approved by the California Department of Motor Vehicles to test autonomous vehicles on the road. In May 2018 a panel of economics experts (University of Chicago, IGM Forum) was asked their opinion about autonomous cars. Only 14% of economists agreed that
According to the Bureau of Labor Statistics, the average workweek for an adult in the United States in April 2018 was 34.5 hours. Assume the population standard deviation for the number of hours worked per week is 5.0 hours. A random sample of 30 U.S. adults worked an average of 35.1 hours last
The concerns about the impact of technology on our lives are growing. There have been recent research reports about the negative impact of digital technology usage on stress, work productivity, happiness, and overall well-being. In light of these concerns, the Pew Research Center asked technology
Student loan debt is the only form of consumer debt that has grown since the peak of consumer debt in 2008. According to the New York Federal Reserve, the average student loan of somebody younger than 30 is $21,750. Assume the standard deviation for debt is $5,000 per student.a. What is the
According to the U.S. Energy Information Administration, regular gasoline averaged $2.65 per gallon in the United States in April 2018. Assume the standard deviation for gasoline prices is $0.12 per gallon. A random sample of 30 service stations was selected.a. What is the probability that the
According to the Bureau of Labor Statistics, the unemployment rate for workers aged 20 to 24 in April 2018 was 6.7%. Consider a random sample of 110 workers from this age group.a. What is the probability that 10 or fewer will be unemployed?b. What is the probability that 5 or fewer will be
According to the Bureau of Labor Statistics, the annual wage for a federal employee in 2017 was $76,250. Assume the population standard deviation is $28,025. A random sample of 34 federal employees is selected.a. What is the probability that the sample mean will be less than $70,000?b. What is the
According to eMarketer.com, 36% of mobile phone users in the United States use the Snapchat app at least once a month (March 2017). A sample of 125 was selected.a. Calculate the standard error of the proportion (round standard error to 4 decimal places).b. What is the probability that less than 30%
First-time buyers are very important to the housing market because these buyers allow existing homeowners to “move up” into their next home. According to the National Association of Realtors, 34% of U.S. homes sold in November 2017 were purchased by first-time buyers. A random sample of 175
According to the Organisation for Economic Cooperation and Development (OECD), adults in the United States worked an average of 1,783 hours in 2016. Assume the population standard deviation is 400 hours and that a random sample of 50 U.S. adults was selected.a. Calculate the standard error of the
According to the Bureau of Labor Statistics, Americans spend on average $2,913 in 2016 on entertainment. Assume the population standard deviation of this spending is $873. A random sample of 31 adults was selected and was found to have an average spending of $2,700 on entertainment.a. Does this
According to statista.com, the average hotel price in Miami, Florida, was $155 per night in 2017. Assume the population standard deviation is $26.00 and that a random sample of 35 hotels was selected.a. Calculate the standard error of the mean.b. What is the probability that the sample mean will be
According to the National Association of Theater Owners, the average price for a movie in the United States in 2017 was $8.97. Assume the population standard deviation is $0.50 and that a sample of 30 theaters was randomly selected.a. Calculate the standard error of the mean.b. What is the
The Excel file titled states.xlsx contains the median income in 2017 for all 50 states, the District of Columbia and Puerto Rico.a. Use Excel to draw a simple random sample consisting of four states, and then calculate the sampling error for the sample.b. Use Excel to draw a simple random sample
The average number of days a house was on the market in Austin, Texas, in 2018 was 61 days (realyaustin. com). Assume the time on the market follows an exponential probability distribution.a. What is the probability that a randomly selected house will be on the market less than 40 days?b. What is
Much of the NCAA men’s basketball tournament, otherwise known as March Madness, takes place during the workweek. According to a survey from marketwatch.com in 2018, 40% of workers say that they always watch March Madness at the office. A random sample of 50 employed adults who plan to watch at
According to data from facebook.com, in 2016 the average amount of time that users spend each day on Facebook, Instagram, and Messenger platforms is 50 minutes. Assume the data for time spent follow the normal distribution with a standard deviation of 14.5 minutes.a. What is the probability that a
Due to the Great Recession (2008–2010), new car sales plunged from 16.9 million cars sold in 2005 to 10.4 million cars sold in 2009. This trend resulted in a significant shortage of used cars during the next few years which, in turn, pushed up used car prices. Suppose that the average price of a
Pew Research Center surveyed adults that were 18–64 years old and had their own children under age 18 living in their household in 2015 on the amount of time spent on various activities. The results indicated that moms spent an average of 25 hours per week doing paid work (compared to 43 hours
Pew Research Center surveyed adults who were 18–64 years old and had their own children under age 18 living in their household in 2015 on the amount of time spent on various activities. The results indicated that dads spent an average of 9 hours per week doing housework (compared to 18 hours per
According to the U.S. Bureau of Labor Statistics, the median weekly real earnings for wage and salary workers 16 years and older in the first quarter of 2018 was $350. Assume weekly wages in the United States follow the normal distribution with a standard deviation of $80.a. What is the probability
According to the Organisation for Economic Co-operation and Development (OECD), South Koreans worked an average of 2,069 hours per year in 2016 (compared with 1,783 for workers in the United States). Assume this random variable follows a normal distribution with a standard deviation of 420 hours.a.
The average U.S. monthly cable bill in 2016 has been reported to be $103. Assume monthly cable bills follow a normal distribution with a standard deviation of $9.50.a. What is the probability that a randomly selected bill will be1. less than $100?2. less than $110?3. exactly $105?4. between $95 and
According to mashable.com, 37% of Snapchat users use the app for Creativity. A random sample of 30 of users was selected. Assuming this estimate is true, use the normal approximation to the binomial distribution to answer the following:a. Calculate the mean and standard deviation for this
According to the Bureau of Transportation Statistics, 81.9% of American Airline flights were on time during 2017. Assume this percentage still holds true for American Airlines. Using the normal approximation to the binomial distribution, determine the probability that of the next 30 American
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