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Business Statistics 2nd Edition Robert A. Donnelly - Solutions
Generation Y has been defined as those individuals who were born between 1981 and 1991. A recent survey by the National Foundation for Credit Counseling found that 58% of the young adults in Generation Y pay their monthly bills on time. Suppose we take a random sample of 200 people from Generation
The following table shows the total points scored in the 16 National Football League games played during Week 1 of the 2012 season.a. Calculate the mean for this population.b. Calculate the sampling error using the first four games in the first row as your samplec. Calculate the sampling error
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, 31% of U. S. homes sold in November 2012 were purchased by first time buyers. A random sample of
According to the Pew Internet & American Life Project, 73% of U. S. teens aged 12– 17 used social networks. A random sample of 130 teenagers from this age group was selected.a. Calculate the standard error of the proportion.b. What is the probability that less than 75% of the teens from this
The Social Media and Personal Responsibility Survey found that 69% of parents are “friends” with their children on Facebook. A random sample of 140 parents was selected.a. Calculate the standard error of the proportion.b. What is the probability that 100 or more parents from this sample are “
On Campus Research recently reported that 46% of college students aged 18– 24 would spend their spring breaks relaxing at home. A sample of 155 college students was selected.a. Calculate the standard error of the proportion.b. What is the probability that less than 40% of the college students
According to the National Retail Federation, 36% of taxpayers used computer software to do their taxes for the 2012 tax year. A sample of 125 taxpayers was selected.a. Calculate the standard error of the proportion.b. What is the probability that less than 30% of the taxpayers from the sample used
Pike Creek Golf Club currently has 375 members who pay annual dues to play golf on the course. Historical records show that 38% of the members use the course at least once a week during the summer season. To verify this, a random sample of 100 members was selected.a. Calculate the standard error of
At Goldey Beacom College, 56% of employees carry dependent family members on their health insurance plans. Currently, there are 200 employees working for the college. A random sample of 50 employees is selected.a. What is the probability that less than 60% of the sample carries dependent family
Managers at a local AT& T Wireless retail center have a goal that 75% of the center’s customers will have to wait less than 5 minutes for service. The Excel file named AT& T.xlsx shows the wait times of a random sample of 160 customers in minutes. Use Excel’s COUNTIF function to count
According to FedSmith. com, the average salary for a federal employee in 2012 was $ 74,804. Assume the population standard deviation is $ 15,300. 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 probability
According to the Bureau of Labor Statistics, the unemployment rate for workers aged 20 to 24 in February 2013 was 13.1%. Consider a random sample of 110 workers from this age group.a. What is the probability that 20 or fewer will be unemployed?b. What is the probability that 15 or fewer will be
Avis rental car in Whittier, Alaska, currently has 15 rental cars on its lot, each with the following mileage:a. Calculate the mean for this population.b. Calculate the sampling error using the five cars in the first row as your samplec. Calculate the sampling error using the 10 cars in the first
One of Super Giant’s grocery stores in Pennsylvania sells, on average, 1,120 cases of Pepsi products a week with a standard deviation of 146 cases. Josh Nelson, who is the Pepsi account manager for this store, receives a bonus if the store’s weekly sales over a four week period during the month
According to the Beverage Marketing Corporation, the per capita consumption of bottled water in the United States is 2.3 gallons per month. Assume the standard deviation for this population is 0.75 gallons per month. Consider a random sample of 36 people.a. What is the probability that the sample
It is commonly known that approximately 10% of the population is left handed. Nike Golf would like to estimate the proportion of left handed golfers in order to plan the schedule of golf club production. Assume Nike collected a sample of 200 golfers.a. What is the probability that more than 12% of
According to AAA, regular gasoline averaged $ 3.68 per gallon in the United States in March 2013. 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 sample mean will be less than $ 3.66?b.
Generation Y has been defined as those individuals who were born between 1981 and 1991. According to the Project on Student Debt, Generation Y students graduating from college averaged $ 23,200 in debt. Assume the standard deviation for debt is $ 7,500 per student.a. What is the probability that
The Journal of American College Health found that 56.4% of college students who lived in coed dormitories consumed alcohol weekly (compared with 26.5% who lived in single sex dormitories). A random sample of 160 students who live in coed dormitories was selected.a. What is the probability that more
A certain unnamed statistics teacher needs to grade 90 exams. The teacher claims that exams require an average of 12 minutes to grade with a standard deviation of 3 minutes. A random sample of 15 exams is selected.a. What is the probability that the sample mean will be more than 11 minutes per
Shortly after the major oil spill in the Gulf of Mexico that occurred in April 2010 due to an explosion on an oil rig, a Rasmussan Poll found that 23% of respondents were against offshore drilling for oil. In an effort to confirm these results, an environmental group randomly selected 200 adults
Many homeowners rely on handymen to perform small jobs, such as repairs or maintenance, around their residence. According to HomeAdvisor Inc., the average cost for a handyman project is $ 460. Assume the population standard deviation is $ 95. A random sample of 30 handyman projects was selected.a.
In an effort to reduce health care costs, many companies are encouraging their employees to walk more. According to the Medicine & Science in Sports & Exercise Journal, Americans take an average of 5,117 steps per day. Assume the population standard deviation is 2,200 steps per day. Jim
The Excel file titled states. xlsx contains the median income in 2011 for all 50 states and the District of Columbia.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 consisting of
According to the Bureau of Labor Statistics, the average workweek for an adult in the United States in February 2013 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 “sandwich generation” is defined as adults who are financially supporting their children while providing care for their aging parents. The number of adults in this category has increased recently with higher unemployment rates, especially for young adults. Financial burdens carried by this
According to the Graduate Management Admission Council, the average starting salary for an MBA graduate in the class of 2011 was $ 85,854. Assume the population standard deviation for starting MBA salaries was $ 11,700. A random sample of 40 MBA graduates from the class of 2011 was selected.a.
Urban planners will use electronic traffic counters to count the number of vehicles that travel on a specific road. This information can be used to identify roads that need to be improved or expanded based on traffic needs. Suppose that, from historical studies, Duncan Road in Kent County averages
Some employers are offering their employees a Consumer Directed Health Plan (CDHP) where the employer provides employees with a sum of money from which employees can purchase their health plan from an online marketplace. The concept is based on the belief that employees will behave more efficiently
Negative equity is defined as a situation where the mortgage on a property is more than the market value of the property. During the recent financial crisis, market values of most homes declined resulting in an increase in the proportion of homes with negative equity. This, in turn, led to an
According to Catalyst, 14.3% executive positions in Fortune 500 companies are occupied by women in 2012. A random sample of 180 Fortune 500 executives was selected.a. What is the probability that 20% or less of this sample were women?b. What is the probability that 18% or more of this sample were
According to the Department of Transportation, the average licensed driver travels 1,123 miles per month in his or her vehicle. Assume the population standard deviation is 341 miles per month. Determine the interval that will contain 95% of the sample means for a sample size ofa. 30 driversb. 45
Obtaining a driver’s license at the earliest eligible age has been a teenage ritual that appears to be fading. A study performed by the University of Michigan Transportation Research Institute recently found that 30% U. S. teenagers between the ages of 17 to 19 did not possess a driver’s
Suppose I am employed at a college in which 62% of the student population is female. I am currently teaching statistics to 135 students this semester. I would like to select 50 students randomly from this group to participate in one of my research projects.a. What is the probability that 30 or more
The Excel file titled verizon.xlsx contains daily revenues for the past 350 business days earned from cell phone accessories (Bluetooth headsets, memory cards, and so on) sold at a local Verizon retail store in Delaware.a. Use Excel to draw a systematic sample consisting of 10 days, and then
Quality control programs will often establish control limits that are three standard errors above and below a target mean for a process. A sample is taken from the process, and if the sample mean is within the control limits the process is deemed satisfactory. A process is designed to fill bottles
The National Center for Health Statistics reported that 34% of Americans were obese recently. The Center for Disease Control estimated that obese people spent an average of $ 1,429 more for medical goods and services than non obese people. Obesity is determined using a formula called body mass
Wawa Corporation operates 570 convenient food stores in Delaware, Maryland, New Jersey, Pennsylvania, and Virginia. Suppose the company’s managers have a goal that customer satisfaction is to average at least 8.0 on a scale of 1– 10. A random sample of 60 stores was selected, and the average
For a population with a mean equal to 150 and a standard deviation equal to 30, calculate the standard error of the mean for a sample size ofa. 10b. 30c. 50
For a normal population with a mean equal to 80 and a standard deviation equal to 15, determine the probability of observing a sample mean of 85 or less from a sample of size 10.
For a population that is left skewed with a mean of 24 and a standard deviation equal to 15, determine the probability of observing a sample mean of 23 or more from a sample of size 32.
Construct a 90% confidence interval to estimate the population mean using the following data:x̅ = 75 σ = 20 n = 36
The average selling price of BlackBerry smartphones purchased by a random sample of 35 customers was $ 311. Assume the population standard deviation was $ 35.a. Construct a 90% confidence interval to estimate the average selling price in the population with this sample.b. What is the margin of
A random sample of 40 taxpayers with adjusted gross incomes of between $ 100,000 and $ 200,000 was drawn. These taxpayers claimed an average of $ 9,922 in medical expenses for the year. Assume the population standard deviation for these deductions was $ 2,400. Construct confidence intervals to
The caloric consumption of 32 American adults was measured and found to average 2,157. Assume the population standard deviation is 260 calories per day. Construct confidence intervals to estimate the mean number of calories consumed per day for the American population with the following confidence
Suppose Apple claims that the average wait time for a customer calling the Apple Care support line is 175 seconds. A random sample of 40 customers had an average wait time of 187 seconds. Assume the population standard deviation for wait time is 50 seconds.a. Using a 95% confidence interval, does
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 C6615DN 25mL black print cartridge will yield an average of
Golf cart attendants at a local country club often receive tips from golfers they assist with their golf clubs. To help recruit new employees, the country club would like to determine the average tips per day an attendant earns. A sample of 16 attendants averaged $ 42.60 per day in tips. Assume the
Toyota Motor Corporation developed the Scion car model to appeal to young consumers. Toyota claims the average age of a Scion driver is 26 years old. Suppose a random sample of 18 Scion drivers was drawn, and the average age of the drivers was found to be 27.5 years. Assume the standard deviation
Construct a 90% confidence interval to estimate the population mean using the following data:x = 25 σ = 5.2 n = 21What assumptions need to be made about this population?
Construct a 95% confidence interval to estimate the population mean using the following data:x = 38 σ = 8.5 n = 25What assumptions need to be made about this population?
Construct a 98% confidence interval to estimate the population mean when = 60 and σ = 12.2 for the following sample sizes:a. n = 20b. n = 40c. n = 60
Construct a 99% confidence interval to estimate the population mean using the following data:x̅ = 45 σ = 30 n = 40
Construct an 80% confidence interval to estimate the population mean when x̅ = 125 and σ = 32 for the following sample sizes:a. n = 30b. n = 60c. n = 90
Determine the margin of error for a confidence interval to estimate the population mean with n = 20 and σ = 16 for the following confidence levels:a. 80%b. 90%c. 99%
Determine the margin of error for a 95% confidence interval to estimate the population mean when σ = 40 for the following sample sizes:a. n = 10b. n = 30c. n = 50
With a capacity of 6,300 people, Royal Caribbean’s Oasis of the Seas is the world’s largest cruise ship. The average beer consumption over 15 randomly selected seven day cruises on the ship was 81,740 bottles with a sample standard deviation of 4,590 bottles. Royal Caribbean would like to
A random sample of 21 NCAA Division I men’s basketball games during a recent season had an average attendance of 5,038 with a sample standard deviation of 1,755.a. Construct a 90% confidence interval to estimate the average attendance of an NCAA men’s basketball game during the 2009– 2010
The U. S. air traffic control system handled an average of 47,529 flights during 30 randomly selected days. The standard deviation for this sample is 6,210 flights per day.a. Construct a 99% confidence interval to estimate the average number of flights per day handled by the system.b. Suppose the
The following data show the number of hours per day 12 adults spent in front of screens watching television related content:1.3 4.9 4.2 4.8 7.6 6.9 5.4 2.2 5.3 1.8 2.4 8.3a. Construct a 95% confidence interval to estimate the
According to Expedia.com, workers in Italy lead the world in paid vacation days, averaging 42 days per year. The following data show the number of paid vacation days for a random sample of 20 Italian workers. These data can also be found in the Excel file titled paid vacation. xlsx.a. Construct a
AAA reported that the average price of regular gasoline in Pennsylvania was $ 3.65 per gallon. The following data show the price per gallon of regular gasoline for 15 randomly selected stations in the state. These data can also be found in the Excel file titled PA gas prices.xlsx.a. Construct a 90%
Construct a 90% confidence interval to estimate the population proportion with a sample proportion equal to 0.36 and a sample size equal to 125.
Construct a 95% confidence interval to estimate the population mean with x̅ = 110 and σ = 30 for the following sample sizes:a. n = 30b. n = 45c. n = 60
Construct a 95% confidence interval to estimate the population proportion with a sample proportion equal to 0.60 and a sample size equal to 150.
Determine the margin of error for a confidence interval to estimate the population proportion for the following confidence levels with a sample proportion equal to 0.40 and n = 100:a. 90%b. 95%c. 97%
Determine the margin of error for a 95% confidence interval to estimate the population proportion with a sample proportion equal to 0.70 for the following sample sizes:a. n = 125b. n = 200c. n = 250
The U. S. Department of Education reported that in 2007, 67% of students enrolled in college or a trade school within 12 months of graduating from high school. In 2013, a random sample of 160 individuals who graduated from high school 12 months prior was selected. From this sample, 102 students
The IRS reported that 81% of individual tax returns were filed electronically in 2012. A random sample of 225 tax returns from 2013 was selected. From this sample, 176 were filed electronically.a. Construct a 95% confidence interval to estimate the actual proportion of taxpayers who filed
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, 29% of high school students applied to seven or more colleges in 2011. A random sample of 350 high school
Although Germany has one of the healthiest economies in the euro zone, it has one of the lowest homeownership rates in Europe. According to ECD, the German homeownership rate was 44% in 2011 (compared to 66% in the United States). Suppose, from a random sample of 270 households in Germany in 2014,
According to the Centers for Disease Control and Prevention, 20.6% of the U. S. population smoked in 2008. In 2014, a random sample of 650 Americans was selected; 108 of whom smoked.a. Construct a 90% confidence interval to estimate the actual proportion of people who smoked in the United States
Determine the sample size needed to construct a 90% confidence interval to estimate the population mean when σ = 75 and the margin of error equals 12.
Determine the sample size needed to construct a 95% confidence interval to estimate the population mean when σ = 40 and the margin of error equals 6.
Construct a 98% confidence interval to estimate the population mean with x̅ = 60 and σ = 12 for the following sample sizes:a. n = 35b. n = 45c. n = 55
Determine the sample size needed to construct a 95% confidence interval to estimate the population mean for the following margins of error when σ = 80: a. 10 b. 15 c. 20
Determine the sample size needed to construct a 99% confidence interval to estimate the population proportion when p = 0.40 and the margin of error equals 5%.
Determine the sample size needed to construct a 90% confidence interval to estimate the population proportion when p = 0.65 and the margin of error equals 6%.
Determine the sample size needed to construct a 95% confidence interval to estimate the population proportion for the following sample proportions when the margin of error equals 4%: a. p = 0.30 b. p = 0.40 c. p = 0.50
Determine the sample size needed to construct a 95% confidence interval to estimate the average GPA for the student population at Wilmington College with a margin of error equal to 0.2. Assume the standard deviation of the GPA for the student population is 1.0. Verify your result using PHStat.
Michelin Tires would like to estimate the average tire life of its Latitude Tour tire in terms of how many miles it lasts. Determine the sample size needed to construct a 98% confidence interval with a margin of error equal to 2,000 miles. Assume the standard deviation for the tire life of this
Herr Foods, a producer of a variety of salty snacks, would like to estimate the average weight of a bag of BBQ potato chips produced during the filling process at its Nottingham, Pennsylvania, plant. Determine the sample size needed to construct a 95% confidence interval with a margin of error
The state of New Jersey would like to estimate the proportion of voters who intend to participate in the upcoming statewide elections. A pilot sample of 50 voters found that 36 of them intended to vote in the election. Determine the additional number of voters that need to be sampled to construct a
Red Fire Grill would like to estimate the proportion of tips that exceed 18% of its dinner bills. Without any knowledge of the population proportion, determine the sample size needed to construct a 90% interval with a margin of error of no more than 4% to estimate the proportion. Verify your result
Suppose Christiana Hospital would like to estimate the proportion of patients who feel that physicians who care for them always communicated effectively when discussing their medical care. A pilot sample of 40 patients found that 33 reported that their physician communicated effectively. Determine
Determine the margin of error for a confidence interval to estimate the population mean with n = 35 and σ = 40 for the following confidence levels:a. 90%b. 95%c. 96%
Construct a 90% confidence interval to estimate the population mean using the following data:x = 70 σ = 20 n = 40 N = 400
Construct a 99% confidence interval to estimate the population mean using the following data:x = 22 σ = 4.5 n = 20 N = 180
Construct a 95% confidence interval to estimate the population proportion using the following data: x̅= 22 n = 75 N = 500
The University of Delaware would like to estimate the proportion of fans who purchase concessions at the first basketball game of the new season. The basketball facility has a capacity of 3,500 people and is routinely sold out. It was discovered that a total of 260 fans out of a random sample of
Radon is a colorless and odorless radioactive gas that can accumulate in residential homes. High levels of exposure can lead to health problems such as lung cancer. Radon levels are measured in units of picocuries per liter (pCi/ L). The recommended radon level from the EPA is less than 4 pCi/L.
Dr. Thomas Bilski is a primary care physician with a practice that is currently serving 280 patients. Dr. Bilski would like to administer a survey to his patients to measure their satisfaction levels with his practice. A random sample of 24 patients had an average satisfaction score of 8.4 on a
According to the Bureau of Labor Statistics, the average hourly wage in the United States was $ 22.57 in May 2010. To confirm this wage, a random sample of 36 hourly workers was selected during the month. The average wage for this sample was $ 21.32. Assume the standard deviation of wages for the
On June 2, 2010, major league pitcher Armando Galarraga of the Detroit Tigers lost his bid for a perfect game when umpire Jim Joyce incorrectly called a runner safe at first base with two outs in the ninth inning. ( A perfect game occurs when a pitcher faces 27 batters without any opposing players
One provision of the Affordable Care Act, commonly known as Obamacare, requires insurance plans pay for breast feeding support for mothers, such as consultations and breast pumps. According to the CDC, 48% of mothers were breast feeding their six month old babies in 2012. Suppose Humana Health
The following data show the costs charged by a tax preparation service for a random sample of 15 tax returns. These data can also be found in the Excel file titled tax prep costs. xlsx.a. Using a 98% confidence interval, estimate the average cost of the service for preparing a tax return for a
Determine the margin of error for an 80% confidence interval to estimate the population mean with σ = 50 for the following sample sizes:a. n = 30b. n = 45c. n = 60
Airline companies recognize that empty seats represent lost revenues that can never be recovered. To avoid losing revenues, the companies often book more passengers than there are available seats. Then, when a flight experiences fewer no shows than expected, some passengers are “ bumped” from
The makers of compact fluorescent light bulbs (CFL) claim the bulbs use 75% less energy and last 10 times longer than incandescent bulbs. A 16 watt CFL (equivalent to a 60 watt incandescent) has a rated lifetime of 8,000 hours. To test this claim, a random sample of 50 CFLs was drawn, and the
Aetna, a major health insurance company, would like to estimate the average wait time for a patient seeking emergency room services. A random sample of 33 emergency room patients had an average wait time of 222 minutes with a sample standard deviation of 76 minutes. Determine the confidence
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