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business statistics
Business Statistics 2nd Edition Robert A Donnelly, Robert Donnelly Jr - Solutions
During 2012, the average monthly bill for digital cable in the United States was $86 according to research firm Centris.Suppose Comcast would like to test the hypothesis that the average monthly bill is higher than $86 this year. A random sample of 52 households was chosen. Assume the standard
According to the U.S. Department of Labor, 12.3% of the U.S. workforce was unionized in 2009. 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
Consider the following observed frequencies:Population Yes No A 20 18 B 10 12 Calculate the expected frequency for each observed frequency.AppendixLO1
Using the data from Problem 12.1, perform a chi-square test using a = 0.05 to determine if the proportion of“Yes” observations differs between Populations A and B.AppendixLO1
Consider the following observed frequencies:Population Yes No A 10 22 B 16 26 C 17 9 Calculate the expected frequency for each observed frequency.AppendixLO1
Using the data from Problem 12.3, perform a chi-square test using a = 0.05 to determine if the proportion of “Yes”observations differs among Populations A, B, and C.Applications AppendixLO1
An important statistic that the Bureau of Labor Statistics(BLS) tracks is the percentage of Americans between the ages of 25 and 54 who are currently working. Suppose a random sample of 100 men in this age group as selected and it was found that 83 were currently working. A similar sample of 100
The federal government would like to determine if the proportion of households without health insurance coverage differs with household income. Suppose the following data were collected from 700 randomly selected households.Health Insurance Household Income Yes No Less than $25,000 57 21 $25,000 to
A survey asked Democrats, Republicans, and Independent voters what the most important message is to send to Congress. One of the most popular responses for all three groups was to “focus on the economy.” The number of respondents, the messages they want sent, and their party affiliations are
An increase in the number of skin cancer cases has raised the awareness of the importance on wearing sunscreen for protection. Suppose the Skin Cancer Foundation surveyed 75 men and found that 35 had not applied sunscreen in the past 12 months. A random sample of 80 women found that 23 had not
Consider the following discrete probability distribution along with observed frequencies for each day of the week:Weekday Probability Observed Frequency, fo Monday 0.10 12 Tuesday 0.20 27 Wednesday 0.05 7 Thursday 0.30 40 Friday 0.35 34 Total 1.00 120a. Perform a chi-square test using a = 0.05 to
Consider the observed frequency distribution for the following set of random variables:Random Variable, x Frequency, fo 0 17 1 35 2 30 3 15 4 and more 3 Total 100 Perform a chi-square test using a = 0.05 to determine if the observed frequencies follow the Poisson probability distribution when l =
Consider the observed frequency distribution for the following set of random variables:Random Variable, x Frequency, fo 0 23 1 60 2 122 3 83 4 12 Total 300a. Perform a chi-square test using a = 0.05 to determine if the observed frequencies follow the binomial probability distribution when p = 0.50
Consider the observed frequency distribution for the following set of grouped random variables:Random Variable, x Frequency, fo Less than 80 10 80 to under 100 14 100 to under 120 19 120 and more 7 Total 50 Perform a chi-square test using a = 0.05 to determine if the observed frequencies follow 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
The following table shows the U.S. market share for automotive manufacturers in 2013 according to Autodata. Also shown is the frequency of car purchases by manufacturer from a random sample of 220 customers during 2014.Manufacturer Market Share 2013 (%)Frequency 2014 General Motors 18.5 35 Ford
In an effort to predict customer arrivals better, the Avalon grocery store counted the number of customers who arrived at the store during randomly selected 10-minute intervals.The following table shows these data. For example, there were 12 10-minute intervals in which no customers arrived, and 27
The following data show the number of touchdown passes thrown by quarterback Aaron Rodgers during 40 games in which he played with the Green Bay Packers. These data can also be found in the Excel file Rodgers.xlsx.1 3 0 2 3 2 1 1 0 2 2 3 2 1 2 3 1 1 2 2 2 3 3 2 1 2 3 3 0 3 1 1 2 2 1 3 1 1 2 0 Using
Suppose that candidates for a job opening at Citibank interview with four different managers. Each manager independently evaluates each candidate with a “yes” or “no”hiring decision. The following table shows the number of“yes” decisions given the last 90 candidates:Number of
Suppose I gave my statistics class a four-question, multiple-choice quiz at the beginning of the semester to measure how well prepared they were for the class. The following table shows the number of students who had 0, 1, 2, 3, and 4 questions correct:Number of Correct Answers per Student
In Chapter 8 we examined confidence intervals. Recall that to construct a confidence interval for the mean when the population standard deviation is unknown, the population must follow the normal probability distribution.To test this condition, the following data show a random sample of weekly
The following data shows the weekly purchases of printers at a particular electronic store. The data can also be found in the Excel file weekly printer demand.xlsx.8 15 12 17 19 12 14 5 8 3 3 15 6 16 15 10 12 17 12 12 6 10 9 10 9 17 8 8 16 6 19 11 3 9 12 7 15 10 14 14 13 10 11 7 17 Using a = 0.05,
Consider a contingency table of observed frequencies with three rows and four columns:a. How many chi-square degrees of freedom are associated with this table?b. What is the chi-square critical value when a = 0.05?c. What is the chi-square critical value when a = 0.10?AppendixLO1
Consider the following contingency table of observed frequencies:Column Variable Row Variable C1 C2 C3 R1 9 7 10 R2 10 7 7a. Identify the null and alternative hypotheses for a chisquare test of independence based on the information in the table.b. Calculate the expected frequencies for each cell in
Consider the following contingency table of observed frequencies:Column Variable Row Variable C1 C2 C3 R1 20 6 18 R2 7 8 11 R3 10 15 5a. Identify the null and alternative hypotheses for a chisquare test of independence based on the information in the table.b. Calculate the expected frequencies for
The following contingency table shows the distribution of grades earned by students taking a midterm exam in an MBA class, categorized by the number of hours the students spent studying for the exam:Grade Time Spent Studying A B C Less than 3 hours 4 18 8 3–5 hours 15 14 6 More than 5 hours 18 12
Suppose Capital One would like to determine if the type of credit card influences the payment status of a customer’s account. The following table indicates the card type for 200 randomly selected customers, along with the number of days their payments were overdue:Card Type Days Overdue Standard
The following table shows the medal count for the United States, Germany, and Great Britain following the 2012 Summer Olympics in London.Medal Country Gold Silver Bronze United States 46 29 29 Germany 11 19 14 Great Britain 29 17 19a. Using a = 0.05, perform a chi-square test to determine if the
Suppose the marketing research firm comScore would like to examine if the social networking site that a person primarily uses is influenced by his or her age. In a randomly drawn sample, 355 social network users were asked which site they primarily visited. These data are presented in the following
The percentage of students from for-profit institutions who have defaulted on their student loans has received much attention recently. Suppose the following data were collected from a random sample of students who graduated three years ago from various types of institutions with student
A survey was conducted to determine by age group the number of registered voters who cast ballots during the recent elections. The following data were recorded:Did You Vote?Age Group Yes No 18–24 18 62 25–34 39 76 35–44 64 76 45–54 54 46 55 and older 82 43a. Using a = 0.01, perform a
Major League Baseball (MLB) records a pitcher’s contact percentage by dividing the number of times batters make contact with the pitches by the number of times they swing at them. The following data represent a sample of this information for three MLB pitchers during the recent season:Number of
Union membership, as a percentage of the working population, varies from country to country. A number of workers from different countries were randomly surveyed and asked whether they belonged to a union. The data from the survey are as follows:Member of Union?Country Yes No France 6 54 United
The U.S. Centers for Disease Control and Prevention(CDC) recommends people consume five servings of fruits and vegetables daily. A random sample of adults from various states was asked if they follow these guidelines. The results are as follows:Follow the CDC Guidelines?State Yes No Delaware 10 30
The following table shows the U.S. market share for smartphone manufacturers in 2013 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 2014.Brand Market Share 2013(%)Observed Frequency 2014 Apple
The following table shows the distribution of the ages of Ohio voters in a 2008 exit poll conducted by Quinnipiac University. The table also shows the observed frequencies from a random sample of Ohio voters by age group in the 2014 midterm elections.Age Group Percentage 2008 Observed Frequency
A survey conducted by Wakefield Research asked adults what their favorite night to order takeout for dinner was. The results are shown in the following table. Suppose a second survey was conducted asking restaurants about the actual observed frequencies for each night’s takeout business. Those
In a Wall Street Journal article titled “Where to Shoot in the Shootout”,4 data were presented about the direction in which penalty shots were kicked toward soccer goals during all of the World Cups since 1998. The following figure shows these data. For example, a total of 37 penalty shots were
The following table shows the frequency distribution for the number of spam e-mails I’ve received over the last 75 days:Number of Spam E-Mails Per Day Frequency 0 12 1 24 2 19 3 12 4 5 5 2 6 1 Total 75a. Using a = 0.10, perform a chi-square test to determine if the number of spam e-mails per day
The following data show the number of employees who called in sick to a chemical plant during the last 50 days.This data can be found in the Excel file sick days.xlsx.2 1 2 3 2 3 0 3 5 2 4 3 1 0 2 0 5 3 1 1 0 2 4 3 2 4 0 0 0 3 3 2 2 1 3 2 3 2 5 3 2 0 1 2 3 0 2 1 0 2 Using a = 0.01, perform a
Chris is a salesperson who makes five sales calls each day to potential customers. Either the customers make a purchase from Chris or they do not. The following table shows the number of days over the past 400 that Chris had 0, 1, 2, 3, 4, or 5 purchases per day.Number of Purchases Per Day
A foursome of golfers plays together routinely. One of the golfers happens to be a statistician who enjoys keeping track of the number of fairways the players hit while teeing off. The following table shows these data for the last 250 holes the golfers have played together:Number of Fairways Hit
A particular weight-loss company claims that the average weight a person lost after two weeks on its program is 5 lbs.The following data represent the weight loss of 36 randomly selected adults who have been on the program for two weeks.Negative values represent weight gains (oops!). These data can
In Chapter 6, I used annual snowfall amounts in Minneapolis from 1884 until 2012 to describe a normal probability distribution. This data can be found in the Excel file snowfall.xlsx.a. Using a = 0.01, perform a chi-square test to determine if the data follow a normal probability distribution.b.
Suppose the Federal Aviation Administration would like to compare the on-time performances of different airlines on domestic, nonstop flights. The following table shows three different airlines and the frequency of flights that arrived early, on time, and late for each:Status Southwest United
A political poll asked potential voters if they felt the economy was going to get worse, stay the same, or get better during the next 12 months. The party affiliations of the respondents were also noted. The results are shown in the following table:Party Affiliation Response Democrat Republican
A random sample of 150 new car buyers who purchased Ford, General Motors (GM), and Chrysler models was selected, and their ages were recorded. The following table shows these data:Age Ford GM Chrysler 20–29 5 11 11 30–39 8 23 7 40–49 16 15 5 50–59 24 15 10a. Using a = 0.05, perform a
Suppose that General Motors gathers from its dealers information about the percentage of new cars that require warranty work during the first year following their sale. Based on these data, GM then compares the dealerships to monitor any unusual patterns. The following table shows the number of
Suppose that Air France would like to determine if the number of lost bags per flight follows the Poisson probability distribution with a mean of 0.7 bags. To test this hypothesis, the following data were collected from 200 randomly selected flights:Number of Lost Bags per Flight Frequency 0 106 1
Suppose that Princess Cruise Lines would like to determine if the satisfaction rating of a customer is related to the number of cruises the person has taken with the company. The following table shows the number of customers who rated their cruises with Princess as Excellent, Good, Average, Fair,
A Gallup poll conducted in 2011 asked respondents why they would not consider buying a hybrid car for their next purchase. The results are shown in the following table.Suppose Toyota would like to confirm these results with its own survey, so the company asked 300 people the same question. The
There has been recent interest in a legislative initiative for laws that ensure paid time off for workers who take sick days. Suppose the Bureau of Labor Statistics (BLS)would like to test if the proportion of workers with paid sick days is influenced by the size of the organization, measured by
Suppose the Federal Communications Commission would like to compare the percentage of the population with access to broadband Internet between Alaska, California, Virginia, and New Mexico. A random sample of 270 adults from these four states was selected and their Internet availability was
A survey conducted by Intermedia reported the percentage of work-related emails sent each day of the work week. To verify Intermedia’s findings, a random sample of work-related emails was selected and the weekday that it was sent was noted. The following table displays these results.Weekday
A particular university includes a capstone course in its MBA program which all graduating students take and covers an overview of topics for their degree. The following contingency table shows the number of students from three different concentrations along with the grade they received in the
Diller & Fisher is a real estate company that rents vacation properties in an ocean-side community in New Jersey. They believe that the following table represents the probability distribution for the number of bedrooms for rental properties.Bedrooms 2 3 4 5 6 Probability 0.12 0.28 0.35 0.15 0.10
Sara is a salesperson for Camera’s Etc. which is a retailer for high-end digital cameras. Historically, Sara has sold an average of 2.1 extended warranties per day. Data in the Excel file camera warranty.xlsx display the number of extended warranties that Sara has sold per day over the past 100
Spencer is the owner of Island Art, a retail establishment in the beach community of Stone Harbor, New Jersey. He would like to develop a probability model to predict the number of customers who visit his establishment each day during the summer season. The Excel file Island Art 1.xlsx shows the
At the beginning of this chapter, the term quadrophobia was defined as the apparent aversion that many firms seem to have of arriving at earnings-per-share calculations that end with the digit “4.” Here’s your chance to investigate the presence of the quadrophobia phenomenon. Suppose you
Consider the following hypothesis statement:H0: s2 Ú 5.0 H1: s2 6 5.0 State your conclusion given that s = 1.6, n = 32, and a = 0.05.AppendixLO1
Consider the following hypothesis statement:H0: s2 … 9.0 H1: s2 7 9.0 State your conclusion given that s = 3.4, n = 25, and a = 0.10.AppendixLO1
Consider the following hypothesis statement:H0: s2 = 12.0 H1: s2 12.0 State your conclusion given that s = 4.6, n = 36, and a = 0.05.AppendixLO1
Consider the following hypothesis statement:H0: s2 = 39.0 H1: s2 39.0 State your conclusion given that s = 6.5, n = 40, and a = 0.05.Applications AppendixLO1
Suppose that on a 100-point test, my goal is for my students’exam scores to have a standard deviation of less than 10 points. A recent sample of 22 exams has a sample standard deviation of 12.1.a. Test whether my goal was achieved using a = 0.05.b. Verify your results using PHStat.c. Interpret
Recently, Seasons Pizza was receiving customer complaints about erratic pizza delivery times. To address this issue, Seasons made some operational changes in its restaurant and added more delivery people to its staff. To study the effectiveness of these changes, Seasons would like to test the
Utz Pretzels produces hard pretzels and packages them in 16-ounce bags. However, the size of each pretzel makes it challenging to fill each bag to precisely 16 ounces. When the filling process is working normally, the standard deviation of the bag weights equals 0.25 ounces. To test if this
Refrigerator manufacturers design their freezer units to maintain temperatures within a certain range. Too much temperature variation can result in food spoiling due to thawing. Too little temperature variation can cause higher energy costs as the refrigerator’s compressor cycles on and off more
Identify the appropriate critical F-score for the following scenarios:a. n1 = 16, n2 = 10, and a = 0.05.b. n1 = 28, n2 = 22, and a = 0.01.c. n1 = 15, n2 = 20, and a = 0.10.AppendixLO1
Consider the following hypothesis statement:H0: s1 2 … s2 2 H1: s1 2 7 s2 2 State your conclusion given that s1 = 18, s2 = 15, n1 = 25, n2 = 20, and a = 0.05.AppendixLO1
Consider the following hypothesis statement:H0: s1 2 = s2 2 H1: s1 2 s2 2 State your conclusion given that s1 = 35, s2 = 30, n1 = 22, n2 = 26, and a = 0.05.AppendixLO1
Consider the following hypothesis statement:H0: s1 2 = s2 2 H1: s1 2 s2 2 State your conclusion given that s1 = 63, s2 = 41, n1 = 25, n2 = 28, and a = 0.05.Applications AppendixLO1
Suppose the Transportation Security Administration is investigating procedures at the Atlanta airport to reduce the variability in the amount of time it takes passengers to get through airport security. The following table summarizes sample data collected from two different terminals employing
Suppose I have two different possible routes for my commute to school. Because I never want to be late for class, I want to choose the route that provides a more consistent commute time. Being a hopeless statistician,I meticulously drove the first route 21 times and the second route 24 times and
Suppose the Goodyear Tire Company developed two new brands of tires and would like to compare the variability of the tire life of the two. Both brands were driven under normal conditions, and random samples of the tires were collected. The following table shows the sample sizes and the standard
The New Jersey teacher’s union would like to see if there is a difference in the variability of the salaries earned by high school teachers in Cape May County as compared with those in Camden County. A random sample of teacher salaries from each county was selected, and the standard deviation of
A high variation in the speed at which cars travel on the interstate can lead to unsafe driving conditions. When some cars are traveling at high speeds and others are traveling at low speeds on the same stretch of highway, the likelihood of an accident increases. Suppose the state of Virginia
According to the Journal of the American Medical Association, a resident doctor worked an average of 59.3 hours per week during 2006–2008. In 2010, the Accreditation Council for Graduate Medical Education, which certifies residency programs in hospitals, developed a plan to reduce the long hours
Purina produces dog food sold in 40-lb. bags. When the filling process is working properly, the standard deviation for the bag weights is 1.4 ounces. The following data represent a random sample of 30 bags from this process. The data can also be found in the Excel file Purina dog food.xlsx.40 38 42
Low-profile tires are automobile tires that have a short sidewall height, which is the distance between the tire rim and the road. These tires provide better performance at the expense of gas mileage. The Ford Taurus was chosen to measure the effect these tires have on the variability of the
In order that patients don’t experience excessive wait times, Aston Medical Center’s goal is for the standard deviation for the time doctors spend with their patients to be less than 6.0 minutes. To determine if this goal is being met, a random sample of times the center’s doctors spent with
Pretzel Boys sells hand-rolled pretzels that are prepared by its employees on the premises. Management would like to ensure that the weight of the pretzels rolled by the employees is consistent by ensuring that the standard deviation for the weight of pretzels is less than 0.04 ounces. The
Susan is shopping for a new golf club that will allow her to hit golf balls more consistently. She is considering Callaway and Nike models. She used a simulator at the golf store to test each club, and the following data were collected.These data can be found in the Excel file
As a customer-satisfaction consistency measure, Tony’s Bistro monitors the size of the tips its waiters receive for serving tables of two customers. The restaurant’s manager believes if the standard deviation of these tips exceeds $3.00, there could be an issue with inconsistent service among
Herr Foods, a producer of a variety of salty snacks, performs taste tests to compare how consumers react to its products. A product such as horseradish cheddar chips is considered a polarizing product because it has a very strong taste. Consumers tend to rate the product very high or very low,
American Airlines and Air France both schedule nonstop flights from Paris to Philadelphia. Suppose you are choosing which airline to fly based on the one with more consistent flight times for the route. For each airline, the following table shows the flight times, in hours, of randomly selected
To help visitors decide which trails are most appropriate for them to hike, the National Park Service (NPS) rates the difficulty of the trails in the nation’s parks. Abrams Falls Trail is a 5-mile trek through Great Smoky Mountains National Park. Suppose the NPS has decided to give Abrams Falls
Edalight is a manufacturer of compact fluorescent lights(CFL) bulbs which are fluorescent bulbs designed to be more efficient than traditional incandescent bulbs. In an effort to produce a consistent product, suppose Edalight has a goal that the standard deviation for the life of its CFL bulbs is
As smartphones have become more sophisticated, their data usage has increased causing capacity issues with service providers. High variability in data usage among customers can result in slow connections with the cellphone network.Suppose Verizon Wireless would like to test if the standard
The pH scale measures the amount of alkalinity or acidity in a liquid and ranges from 0 to 14. The ideal pH for a swimming pool is 7.2. A pH that is too high or low can cause discomfort for the swimmers, especially in the eyes.Chemicals need to be added to the water to adjust the pH to the desired
Traveler’s Insurance would like to investigate if the average number of miles driven per month by a male teenage driver exceeds the average number of miles driven per month by a female teenage driver. The following data summarizes the sample statistics for the miles driven per month by each
Bank of New York would like to determine if the average checking account balance for younger customers (under 40 years) is different from the average checking account balance for older customers (40 or more years). These data can be found in the Excel file checking accounts.xlsx.a. Recall that
Suppose one of the products manufactured by Pittsburgh Plate and Glass (PPG) is a glass pane that is 3/8 in., thick.One of the quality control measurements is the variability in the thickness of the glass panes. If the standard deviation for the thickness of the glass exceeds 0.01 in., the process
The Excel file golf scores.xlsx contains a random sample of golf scores for two highly competitive sons of a certain statistics author. Each son claims he is the more consistent golfer.a. Perform a hypothesis test using a = 0.05 to determine if there is a difference in the variability of the two
Coke would like to perform a blind taste test between its cola and the cola produced by its biggest competitor, Pepsi.To conduct this test, 24 individuals were randomly selected and asked to taste the Coke product and rate it on a scale of 1–10. Another 24 individuals were asked to taste and rate
Consider the following hypothesis statement using a = 0.05 and data from two independent samples:H0: m1 - m2 = 0 H1: m1 - m2 0 x1 = 237 x2 = 218 s1 = 54 s2 = 63 n1 = 42 n2 = 35a. Calculate the appropriate test statistic and interpret the result.b. Calculate the p-value and interpret the result.c.
Consider the following hypothesis statement using a = 0.10 and data from two independent samples:H0: m1 - m2 … 0 H1: m1 - m2 7 0 x1 = 86 x2 = 78 s1 = 24 s2 = 18 n1 = 50 n2 = 55a. Calculate the appropriate test statistic and interpret the result.b. Calculate the p-value and interpret the result.c.
Consider the following hypothesis statement using a = 0.01 and data from two independent samples:H0: m1 - m2 Ú 0 H1: m1 - m2 6 0 x1 = 122 x2 = 139 s1 = 39 s2 = 33 n1 = 40 n2 = 45a. Calculate the appropriate test statistic and interpret the result.b. Calculate the p-value and interpret the
Consider the following data from two independent samples.Construct a 95% confidence interval to estimate the difference in population means.x1 = 24 x2 = 21 s1 = 6 s2 = 5 n1 = 38 n2 = 32 AppendixLO1
Consider the following data from two independent samples.Construct a 90% confidence interval to estimate the difference in population means.x1 = 46 x2 = 53 s1 = 10 s2 = 12 n1 = 30 n2 = 36 Business Applications AppendixLO1
The following data show the average monthly utility bills for a random sample of households in Baltimore and for a random sample of households in Houston. (The bills include phone, television, Internet, electricity, and natural gas.)Baltimore Houston Sample mean $390.44 $359.52 Sample size 33 36
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