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business statistics
Business Statistics 2nd Edition Robert A Donnelly, Robert Donnelly Jr - Solutions
Answer the following questions using the data from Problem 14.53:a. Using a = 0.05, test the significance of the regression slope.b. Construct a 95% confidence interval for the population slope.c. What conclusions about battery life and screen size can be drawn from these results?AppendixLO1
As a measure of productivity, Verizon Wireless records the number of customers each of its retail employees activates weekly. An activation is defined as either a new customer signing a cell phone contract or an existing customer renewing a contract. The following table shows the number of weekly
Answer the following questions using the data from Problem 14.56:a. Calculate the correlation coefficient for this sample.b. Using a = 0.01, test to determine if the population correlation coefficient is not equal to zero.c. What conclusions can be made based on these results?AppendixLO1
Answer the following questions using the data from Problem 14.56:a. Calculate the coefficient of determination.b. Using a = 0.01, test the significance of the population coefficient of determination.c. Construct a 99% confidence interval for the average number of activations made by an employee
Answer the following questions using the data from Problem 14.56:a. Using a = 0.01, test for the significance of the regression slope.b. Construct a 99% confidence interval for the population slope.c. What conclusions about the number of weekly activations and job satisfaction can be drawn from
The American Board of Family Medicine would like to investigate the theory that a mother’s shoe size can be used to predict an infant’s birth weight in pounds. The following table records a random sample of the shoe sizes of 10 mothers and the birth weights of their infants. These data can also
Answer the following questions using the data from Problem 14.60:a. Calculate the correlation coefficient for this sample.b. Using a = 0.10, test to determine if the population correlation coefficient is greater than zero.c. What conclusions can be made based on these results?AppendixLO1
Answer the following questions using the data from Problem 14.60:a. Calculate the coefficient of determination.b. Using a = 0.10, test the significance of the population coefficient of determination.c. Construct a 90% confidence interval for the average birth weight for a maternal shoe size of
Answer the following questions using the data from Problem 14.60:a. Using a = 0.10, test for the significance of the regression slope.b. Construct a 90% confidence interval for the population slope.c. What conclusions about the maternal shoe size and birth weight can be drawn from these results?d.
Zagat surveys airline customers on a 30-point satisfaction scale measuring comfort, service, and food for both domestic and international flights. The Excel file Zagat.xlsx contains survey results that were recently collected showing the average scores for various airlines.a. Calculate the
A regional manager at Acme Markets would like to develop a model to predict weekly sales of pet food based on the shelf space. The following table shows the data collected from nine randomly selected stores and can also be found in the Excel file Acme.xlsx.Shelf Space(Feet)Sales($100)Shelf
Answer the following questions using the data from Problem 14.65:a. Calculate the correlation coefficient for this sample.b. Using a = 0.05, perform a hypothesis test to determine if the correlation coefficient is greater than zero.c. What conclusions can be drawn based on these results?AppendixLO1
Answer the following questions using the data from Problem 14.65:a. Calculate the coefficient of determination.b. Using a = 0.05, test the significance of the population coefficient of determination.c. Construct a 95% confidence interval for the average sales from 4.0 feet of shelf space.d.
Answer the following questions using the data from Problem 14.65:a. Using a = 0.05, test for the significance of the regression slope.b. Construct a 95% confidence interval for the population slope.c. What conclusions about the shelf space and sales can be drawn from these results?d. Verify your
Suppose I recorded the attendance of my students in a recent statistics class because I wanted to investigate the linear relationship between the number of classes they missed and their final grades. The following table shows these data for a random sample of nine students and can also be found in
Answer the following questions using the data from Problem 14.69:a. Calculate the correlation coefficient for this sample.b. Using a = 0.05, perform a hypothesis test to determine if the correlation coefficient is less than zero.c. What conclusions can be drawn based on these results?AppendixLO1
Answer the following questions using the data from Problem 14.69:a. Calculate the coefficient of determination.b. Using a = 0.05, test the significance of the population coefficient of determination.c. Construct a 95% confidence interval for the average grade of students who missed two classes.d.
Answer the following questions using the data from Problem 14.69:a. Using a = 0.05, test for the significance of the regression slope.b. Construct a 95% confidence interval for the population slope.c. What conclusions about missed classes and final grade can be drawn from these results?d. Verify
Suppose GNC, a vitamin and supplement supplier, would like to investigate the relationship between the size of an order and the age of the customer who ordered it. This information could allow GNC to target its promotions to specific age groups. The following table shows the ages for seven randomly
Answer the following questions based on the data from Problem 14.73.a. Calculate the slope and the y-intercept for the regression equation.b. Predict the order size of a 32-year-old customer.c. Provide an interpretation for the value of the slope.d. Calculate the total sum of squares.e. Partition
Answer the following questions based on the data from Problem 14.73.a. Calculate the coefficient of determination.b. Test the significance of the population coefficient of determination using a = 0.05.c. Construct a 95% confidence interval for the average order size for a 40-year-old customer.d.
Answer the following questions based on the data from Problem 14.73.a. Test for the significance of the regression slope using a = 0.05.b. Construct a 95% confidence interval for the population slope.c. What conclusions about the order size and customer’s age can be drawn from these results?d.
A Buick dealership would like to develop a regression model that would predict the number of cars sold per month by a dealership employee based on the employee’s number of years of sales experience. The following regression output was developed based on a random sample of employees.Anova df SS
Mike Lynch manages a real estate firm in Myrtle Beach, South Carolina, and would like to construct a model to help him predict the selling price of beach properties for his customers based on the age of the house in years. Mike has collected a random sample of home sales from the area and generated
Each week during the NCAA men’s college basketball season, teams are ranked according to two polls—the AP Poll and the Coach’s Poll. Each team’s position is determined by the number of points received by the polls. The Excel file NCAA basketball.xlsx lists the points 24 teams received for
Consider the following discrete probability distribution:Outcome Probability 0 0.06 1 0.11 2 0.24 3 0.27 4 0.20 5 ?Determine the missing probability for the random variable that equals 5.AppendixLO1
Consider the following discrete probability distribution:Outcome Probability 1 0.18 2 0.25 3 0.35 4 0.22a. Calculate the mean of this distribution.b. Calculate the standard deviation of this distribution.AppendixLO1
Consider the following discrete probability distribution:Outcome Probability 10 0.10 15 0.30 20 0.20 25 0.30 30 0.10a. Calculate the mean of this distribution.b. Calculate the standard deviation of this distribution.AppendixLO1
The following table provides five different distributions for the daily demand for loaves of sourdough bread at a local bakery. Identify which distributions are valid discrete probability distributions and which ones are not.Explain your answers.Daily Demand Probability Distributions A B C D E 0
A survey recorded the number of children 18 years old or younger who lived in 200 households. The following table shows the results:Number of Children Number of Families 0 88 1 40 2 42 3 20 4 7 5 3a. Determine the mean number of children per household.b. Determine the standard deviation for the
Steve Blass owns two fast-food restaurants in Delaware:one located in Stanton and another located in Newark.Steve has recorded customer satisfaction ratings for both locations on a scale of 1 to 5 15 = Most satisfied2. The following table summarizes the data:Number of Customers Rating Stanton
The following table shows the discrete probability distribution for the number of bedrooms per house in a certain community:Number of Bedrooms Probability 3 0.23 4 0.57 5 0.14 6 0.06a. Determine the mean number of bedrooms per house.b. Determine the standard deviation for the number of bedrooms per
Kohls Candy Company developed a new consumer product that is expected to earn $4,000 in profit each year if consumer demand is low, $20,000 per year if consumer demand is moderate, and $36,000 per year if consumer demand is high. The probability of low, moderate, and high demand is 30%, 45%, and
Avalon Bakery would like you to recommend how many loaves of its famous marble rye bread to bake at the beginning of the day. Each loaf costs the bakery $3.00 and can be sold for $6.00. Leftover loaves at the end of each day are donated to charity. Research has shown that the probabilities for
Consider a binomial probability distribution with p = 0.60 and n = 7. Determine the following probabilities:a. P1x = 22b. P1x … 12c. P1x 7 52 AppendixLO1
Consider a binomial probability distribution with p = 0.35 and n = 8. Determine the following probabilities:a. exactly three successesb. less than three successesc. six or more successes AppendixLO1
Consider a binomial probability distribution with p = 0.25. Determine the probability of exactly four successes for the following conditions:a. n = 5b. n = 7c. n = 10 AppendixLO1
Consider a binomial probability distribution with p = 0.65 and n = 15. Determine the mean and standard deviation of this distribution.Applications AppendixLO1
If a student estimated that the probability of correctly answering each question in a multiple-choice question is 80%, use the binomial tables to determine the probability of earning at least a 70% grade on a 20-question exam.AppendixLO1
A recent survey taken by Adecco of 1,047 employees found that 28% of them would lay off their bosses if they could. Answer the following questions based on a random sample of 10 employees:a. What is the probability that exactly three employees would lay off their bosses?b. What is the probability
A hotel claims that 90% of its customers are very satisfied with its service. Answer the following questions based on a random sample of eight customers:a. What is the probability that exactly seven customers are very satisfied?b. What is the probability that more than seven customers are very
According to a survey by Apartments.com, 35% of apartment renters in 2013 had owned a home at one point.Consider a random sample of nine apartment renters.a. What is the probability that exactly three renters from this sample previously owned a home?b. What is the probability that less than four
According to Catalyst, based on a survey of Fortune 500 companies, 14% of Executive Officer positions in 2012 were female. Answer the following questions based on a random sample of 12 corporate officers:a. What is the probability that one corporate officer was female?b. What is the probability
An e-commerce Web site claims that 6% of people who visit the site make a purchase. Answer the following questions based on a random sample of 15 people who visited the Web site.a. What is the probability that none of the people will make a purchase?b. What is the probability that less than three
Consider a Poisson probability distribution with l = 3.0.Determine the following probabilities.a. P1x = 32b. P1x … 22c. P1x 7 42 AppendixLO1
Consider a Poisson probability distribution with l = 4.7.Determine the following probabilities.a. exactly five occurrencesb. more than six occurrencesc. three or fewer occurrences AppendixLO1
Consider a Poisson probability distribution. Determine the probability of exactly four occurrences for the following conditions:a. l = 2.0b. l = 3.0c. l = 4.0d. What conclusions can be made about how these probabilities change with l?AppendixLO1
Consider a Poisson probability distribution with l = 8.5.Determine the mean and standard deviation of this distribution.Applications AppendixLO1
Assume the number of births in a local hospital follows a Poisson distribution and averages 2.6 per day.a. What is the probability that no births will occur today?b. What is the probability that less than four births will occur today?c. What is the probability that more than one birth will occur
Sara is a salesperson for Camera’s Etc. which is a retailer for high-end digital cameras. Historically, Sara has averaged selling 2.1 extended warranties per day for cameras that she sells. Assume the number of camera warranties that Sara sells per day follows the Poisson distribution.a. What is
A particular intersection in Delaware is equipped with a surveillance camera. The number of traffic tickets issued to drivers passing through the intersection follows the Poisson distribution and averages 4.5 per month.a. What is the probability that seven traffic tickets will be issued at the
A customer support center for a computer manufacturer receives an average of 1.5 phone calls every 5 minutes.Assume the number of calls received follows the Poisson distribution.a. What is the probability that no calls will arrive during the next 5 minutes?b. What is the probability that three or
Production records indicate that 1.5% of the light bulbs produced in a facility are defective. A random sample of 22 light bulbs was selected.a. Use the binomial distribution to determine the probability that two defective bulbs are found.b. Use the Poisson approximation to the binomial
Consider a hypergeometric probability distribution with n = 5, R = 6, and N = 12. Calculate the following probabilities:a. P1x = 32b. P1x = 22c. P1x … 12d. Calculate the mean and standard deviation of this distribution.AppendixLO1
Consider a hypergeometric probability distribution with n = 3, R = 5, and N = 9. Calculate the following probabilities:a. P1x = 02b. P1x 7 12c. P1x 6 32d. Calculate the mean and standard deviation of this distribution.AppendixLO1
An urn contains six blue balls and eight yellow balls. If four balls are selected randomly without being replaced, what is the probability that of the balls selected, three of them will be blue and one of them will be yellow?Applications AppendixLO1
I find a bowl of Christmas M&M’s (only red and green) that Deb has hidden from me in the house one day. I quickly grab a handful before being caught. Before shoving them into my mouth to get rid of the evidence, I notice that I have selected six red M&M’s and no green ones. Let’s say there
White boxers are dogs that have a genetic disposition for going deaf within the first year after they are born. Suppose a litter of nine white boxer puppies contained two dogs that would eventually experience deafness. A family randomly selected two puppies from this litter to take home as family
A political committee consists of seven Democrats and five Republicans. A subcommittee of six people needs to be formed from this group. Determine the probability that this subcommittee will consist of the following:a. Two Democrats and four Republicans if they were randomly selectedb. Four
I have a statistics class of 20 students, of whom 12 are female. I randomly select three students to make a group presentation to the class. What is the probability of the following occurring?a. All of the students in the group are male.b. One of the students in the group is male.c. Two of the
AIG, an international insurance and financial services organization, recently announced that the performance of employees would be rated on a scale from 1 to 4. The top 10% of employees would receive a 1 rating, 20% of the employees would be rated with a 2, and 50% would be rated with a 3. The
The following distribution list displays the number of no-shows for a particular Delta Airlines flight and the historical probability that each number of no-shows will occur. A no-show is a person who has a reservation for a flight but fails to arrive prior to its departure.No-Shows Probability 0
A survey was conducted to determine the number of cats living in individual households. The results are summarized in the following table:Number of Cats Probability 0 0.37 1 0.28 2 0.21 3 0.10 4 0.04a. Determine the mean number of cats per household.b. Determine the standard deviation for the
I am currently teaching two statistics classes, one at 8:00 a.m. and the other at 10:00 a.m. The following table summarizes my attendance records by showing the probability of the number of absent students per class:Probability Number of Absent Students 8 a.m. Class 10 a.m. Class 0 0.06 0.16 1 0.19
An investor has two portfolios to consider. Portfolio A is more heavily invested in bonds, whereas Portfolio B contains more stocks. The following table provides the annual returns for both portfolios under three different market conditions as well as the probability for each market condition in
Tees R Us, which manufactures and sells T-shirts for sporting events, is providing shirts for an upcoming tournament.Each shirt will cost $10 to produce and will be sold for $16.Any unsold shirts left over at the end of the tournament can be sold for $5 apiece in the near future. Tees R Us assumes
The following table shows Bob’s Bookstore’s estimated demand for a new calendar. The bookstore needs to decide whether to order 100, 200, or 300 calendars for the start of the year. Each calendar costs the store $6 to purchase and can be sold for $14. The store can sell any unsold calendars
At the start of each Super Bowl, the NFL championship game between the winners of the NFC and AFC, a coin toss determines the team that will receive the opening kickoff.The NFC team won the coin toss 14 straight years from 1998 until 2011. Determine the probability of one team winning this coin
A recent survey found that only 45% of Americans were satisfied with their current jobs. Answer the following questions based on a random sample of 15 American workers:a. What is the probability that exactly six employees were satisfied with their current jobs?b. What is the probability that
The Center for Disease Control and Prevention estimated that 37% of Americans received a flu shot during the winter of 2012–2013. A random sample of seven Americans was selected.a. What is the probability that exactly four people from this sample received a flu shot that winter?b. What is the
A golfer claims that 80% of the time, he will score less than 90 on the golf course he normally plays. Consider his next 10 rounds of golf.a. What is the probability that he will score lower than 90 on all 10 rounds?b. What is the probability that he will score lower than 90 on eight or more
In 2012, 79% of Southwest Airlines flights arrived at their destinations on time. Suppose a random sample of 12 Southwest Airlines flights was selected.a. What is the probability that all 12 flights were on time?b. What is the probability that more than nine flights were on time?c. What is the
According to the University Business Officers, 86% of first-time, full-time freshman at private colleges were the recipients of some form of financial aid in 2011. A random sample of six freshmen in 2011 was selected.a. What is the probability that all six freshmen from this sample received
According to the Pew Research Center, 23% of American adults read an e-book during 2012. A random sample of nine adults was selected.a. What is the probability that exactly two adults from this sample read an e-book last year?b. What is the probability that less than four adults from this sample
A first draft of a 400-page manuscript has 36 typos that are spread randomly across the pages. Assume the number of typos per page follows the Poisson distribution.a. What is the probability that there is one typo in the first 10 pages?b. What is the probability that there is one typo in the first
Customers arrive at a local ice cream stand at an average rate of 16 per hour and follow a Poisson distribution.a. What is the probability that two customers will arrive during the next 15 minutes?b. What is the probability that four customers will arrive during the next 15 minutes?c. What is the
According to the Department of Transportation, United Airlines lost an average of 3.87 bags per 1,000 passengers during 2012. Assume the number of lost bags follows the Poisson distribution.a. What is the probability that, over the next 1,000 United passengers, nobody will lose their bag?b. What is
According to the National Hurricane Center, the average number of hurricanes during the Atlantic season, which runs from June 1 to November 30, was 6.5 hurricanes per year from 1982 to 2012. Assume the number of hurricanes per year follows the Poisson distribution.a. What is the probability that
Harv& Marv’s Outback Alaska provides personalized 4-hour or 8-hour whale watching tours in Juneau Alaska.(Count Deb and I as two very satisfied customers.) Suppose the number of whales spotted during a 4-hour tour follows the Poisson distribution and averages 5.3.a. What is the probability that
According to hybridcars.com, the market share of hybrid cars in the United States in February 2013 is 3.4%. Consider a random sample of 20 cars in the United States.a. Use the binomial distribution to determine the probability that there are no hybrid cars from this sample.b. Use the binomial
The U.S. Census reports that 3.5% of households have at least three generations living under one roof. Consider a random sample of 24 households.a. Use the binomial equation to determine the probability that three households have at least three generations living in the same house.b. Use the
A grocery store has 18 two-liter bottles of diet cola on the shelf, four of which have exceeded their shelf-life date. You randomly select three bottles of diet cola without checking the expiration date. Determine the probability of the following:a. None of the bottles have exceeded their
An IRS agent has 19 tax returns on her desk, of which 14 were filed using the short form (1040A). She randomly chooses eight returns to audit. Determine the probability of the following:a. All eight were filed using the short form.b. At least six were filed using the short form.c. Explain why it is
My department at school is comprised of 10 faculty and 6 administrators. I need to organize a committee of six people from the department. If I randomly select these committee members, determine the probability that the committee consists of the following:a. Two faculty and four administersb. Four
Winner Automotive has a current inventory of 14 used cars and 8 used trucks. Management needs to select 10 used vehicles to participate in a special used vehicle sale at the local shopping mall. If the vehicles are selected randomly, determine the probability of the following occurring:a. Four
In a standard 52-deck of cards, there are 12 face cards consisting of four jacks, queens, and kings. You are randomly dealt a five-card hand from the deck. What is the probability that your hand will contain the following?a. No face cardsb. One face cardc. Two face cardsd. Four face cardse.
For a standard normal distribution, determine the following:a. P1z … 1.502b. P1z … -1.222c. P1 -0.86 … z … 1.762d. P10.32 … z … 2.152 AppendixLO1
For a standard normal distribution, determine the following:a. P1z 7 1.352b. P1z 7 -0.422c. P1 -1.70 … z … -0.652d. P1 -1.69 … z … 0.202 AppendixLO1
A random variable follows the normal probability distribution with a mean of 80 and a standard deviation of 20.What is the probability that a randomly selected value from this populationa. is less than 90?b. is less than 65?c. is more than 110?d. is more than 40?AppendixLO1
A random variable follows the normal probability distribution with a mean of 124 and a standard deviation of 27. What is the probability that a randomly selected value from this populationa. is between 100 and 140?b. is between 130 and 170?c. is between 65 and 90?d. is between 120 and
A binomial distribution has p = 0.60 and n = 40.a. What are the mean and standard deviation for this distribution?b. What is the probability of exactly 27 successes?c. What is the probability of less than 30 successes?d. What is the probability of more than 20 successes?AppendixLO1
A binomial distribution has p = 0.22 and n = 75.a. What are the mean and standard deviation for this distribution?b. What is the probability of exactly 11 successes?c. What is the probability of 10 to 18 successes?d. What is the probability of 8 to 15 successes?Applications AppendixLO1
The average number of miles driven on a full tank of gas in a Hyundai Veracruz before its low-fuel light comes on is 320. Assume this mileage follows the normal distribution with a standard deviation of 30 miles. What is the probability that, before the low-fuel light comes on, the car will
According to a recent survey by Smith Travel Research, the average daily rate for a luxury hotel in the United States is$237.22. Assume the daily rate follows a normal probability distribution with a standard deviation of $21.45.a. What is the probability that a randomly selected luxury hotel’s
Major League Baseball teams have become concerned about the length of games. During a recent season, games averaged 2 hours and 52 minutes (172 minutes) to complete.Assume the length of games follows the normal distribution with a standard deviation of 16 minutes.a. What is the probability that a
A study conducted by Hershey’s discovered that Americans consumed an average of 11.4 pounds of chocolate per year (seems low to me). Let’s assume that the annual chocolate consumption follows the normal distribution with a standard deviation of 3.6 pounds.a. What is the probability that I will
According to the Internal Revenue Service, the average income tax refund for the 2011 tax year was $2,913. Assume the refund per person follows the normal probability distribution with a standard deviation of $950.a. What is the probability that a randomly selected tax return refund from the 2011
Assume the cost of an extended 100,000 mile warranty for a particular SUV follows the normal distribution with a mean of $1,600 and a standard deviation of $75.a. Determine the interval of warranty costs from various companies that are 1. one standard deviation around the mean.2. two standard
The average price of a 42-in. television on Best Buy’s Web site is $790. Assume the price of these televisions follows the normal distribution with a standard deviation of $160.a. What is the probability that a randomly selected television from the site sells for 1. less than $700?2. between $400
A credit score measures a person’s creditworthiness.According to the credit-scoring company Experian, the average credit score for Americans in march 2013 was 736. Assume the scores are normally distributed with a standard deviation of 40. Determine the interval of credit scores that area. one
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