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business statistics
Business Statistics 2nd Edition Robert A Donnelly, Robert Donnelly Jr - Solutions
Suppose the Bureau of Labor Statistics would like to investigate if the average retirement age for a worker in Japan is higher than the average retirement age for a worker in the United States. A random sample of 30 retired U.S. workers had an average retirement age of 64.6 years. A random sample
Walmart has an interest in monitoring the average backto-school spending for grade-school students year to year.The following table shows the average back-to-school spending of households randomly sampled in 2013 and 2014 along with the population standard deviations and sample sizes for each
Salary data from two random samples of high school teachers from Pennsylvania and Ohio are as follows. Also shown are the population standard deviations for these populations.Pennsylvania Ohio Sample mean $53,289 $49,945 Sample size 40 46 Population standard deviation $6,433 $7,012a. Construct a
Consider the following hypothesis statement using a = 0.05 and data from two independent samples. Assume the population variances are equal and the populations are normally distributed.H0 : m1 - m2 = 0 H1 : m1 - m2 0 x1 = 14.3 x2 = 12.8 s1 = 2.7 s2 = 3.3 n1 = 20 n2 = 18a. Calculate the
Consider the following hypothesis statement using a = 0.05 and data from two independent samples. Assume the population variances are equal and the populations are normally distributed.H0 : m1 - m2 … 10 H1 : m1 - m2 7 10 x1 = 76.3 x2 = 61.5 s1 = 18.4 s2 = 18.7 n1 = 16 n2 = 20a. Calculate the
Consider the following hypothesis statement using a = 0.05 and data from two independent samples. Assume the population variances are not equal and the populations are normally distributed.H0 : m1 - m2 = 0 H1 : m1 - m2 0 x1 = 114.7 x2 = 122.0 s1 = 24.6 s2 = 14.3 n1 = 14 n2 = 20a. Calculate the
Consider the following hypothesis statement using a = 0.10 and data from two independent samples. Assume the population variances are not equal and the populations are normally distributed.H0 : m1 - m2 Ú 0 H1 : m1 - m2 6 0 x1 = 144.0 x2 = 156.3 s1 = 16.8 s2 = 27.0 n1 = 27 n2 = 21a. Calculate the
Consider the following data from two independent samples with equal population variances. Construct a 95%confidence interval to estimate the difference in population means. Assume the population variances are equal and that the populations are normally distributed.x1 = 37.2 x2 = 32.5 s1 = 8.9 s2 =
Consider the following data from two independent samples with equal population variances. Construct a 90%confidence interval to estimate the difference in population means. Assume the population variances are equal and that the populations are normally distributed.x1 = 68.7 x2 = 75.1 s1 = 12.5 s2 =
The following table shows the average hourly wage rates for day-care centers from the Northeast and Midwest regions of the United States based on two random samples:Northeast Midwest Sample mean $9.60 $8.60 Sample standard deviation $1.25 $1.20 Sample size 26 31a. Perform a hypothesis test using a
The following table shows the results of two random samples that measured the average number of minutes per charge for AA Lithium-ion (Li-ion) rechargeable batteries versus Nickel–Metal Hydride (NiMH) rechargeable batteries:Li-ion NiMH Sample mean 96.5 82.9 Sample standard deviation 6.5 11.2
An online travel agent who specializes in cruises wanted to compare the cost of cruising to different destinations on various cruise lines. The following random sample data show the average cost of a seven-day cruise in a standard room to Alaska vs. the average cost of a seven-day cruise in a
The following table shows the average number of words understood by later-born and first-born one-year-old children from two random samples. Assume the population variances of the number of words understood are equal.Later-Born First-Born Sample mean 430.2 552.0 Sample standard deviation 130.8
The following two samples were collected as matched pairs:Pair 1 2 3 4 5 6 7 Sample 1 5 6 9 4 6 7 8 Sample 2 4 2 6 6 5 9 6a. State the null and alternative hypotheses to test if a difference in means exists between the populations represented by Samples 1 and 2.b. Calculate the appropriate test
The following two samples were collected as matched pairs:Pair 1 2 3 4 5 6 Sample 1 7 6 9 5 6 8 Sample 2 4 2 6 6 1 8a. State the null and alternative hypotheses to test if the population represented by Sample 1 has a higher mean than the population represented by Sample 2.b. Calculate the
The following two samples were collected as matched pairs:Pair 1 2 3 4 5 6 7 8 Sample 1 8 4 6 9 9 7 9 8 Sample 2 4 2 6 6 1 8 1 4a. State the null and alternative hypotheses to test if the population represented by Sample 1 has a mean that is 2.0 units higher than the population represented by
The following two samples were collected as matched pairs:Pair 1 2 3 4 5 6 7 Sample 1 8 4 6 9 9 7 9 Sample 2 4 2 6 5 1 8 1a. Construct a 95% confidence interval to estimate the difference in means between the populations from which Samples 1 and 2 were drawn.b. What conclusions can be made based on
The following two samples were collected as matched pairs:Pair 1 2 3 4 5 6 7 8 Sample 1 8 4 6 9 9 7 9 8 Sample 2 5 7 6 5 6 9 7 6a. Construct a 90% confidence interval to estimate the difference in means between the populations from which Samples 1 and 2 were drawn.b. What conclusions can be made
Swype is an input technique for touch-screen devices that allows users to input a word by sliding a finger from letter to letter. The user’s finger is only removed from the keyboard between words. The following table shows the typing speeds of 10 individuals who were measured typing using both
The MCAT is a standardized test used by medical schools in the admissions process. The scale of this exam ranges from 3 to 45. A new type of review course for the MCAT was developed by a training company. The following table shows MCAT scores for nine students before and after taking the review
A new weight-loss program claims that participants will lose an average of more than 10 lbs after completing it.The following table shows the weights of eight individuals before and after the program. These data can also be found in the Excel file weight loss.xlsx.Person 1 2 3 4 5 6 7 8 Before 227
The following table shows the golf scores of nine people before and after a lesson given by the golf professional at Pike Creek Golf Club. These data can also be found in the Excel file lessons.xlsx.Golfer 1 2 3 4 5 6 7 8 9 Before lesson 96 88 94 86 102 90 100 90 99 After lesson 88 81 95 79 95 85
Consider the following hypothesis statement using a = 0.10 and the following data from two independent samples:H0: p1 - p2 Ú 0 H1: p1 - p2 6 0 x1 = 60 x2 = 72 n1 = 150 n2 = 160a. 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 = 0.02 and the following data from two independent samples:H0: p1 - p2 … 0.20 H1: p1 - p2 7 0.20 x1 = 190 x2 = 118 n1 = 225 n2 = 200a. Calculate the appropriate test statistic and interpret the result.b. Calculate the p-value and interpret the
Consider the following hypothesis statement using a = 0.05 and the following data from two independent samples:H0: p1 - p2 = 0 H1: p1 - p2 0 x1 = 18 x2 = 24 n1 = 85 n2 = 105a. Calculate the appropriate test statistic and interpret the result.b. Calculate the p-value and interpret the result.c.
Consider the following data from two independent samples.Construct a 90% confidence interval to estimate the difference in population proportions.x1 = 46 x2 = 48 n1 = 90 n2 = 80 AppendixLO1
Consider the following data from two independent samples.Construct a 90% confidence interval to estimate the difference in population proportions.x1 = 92 x2 = 76 n1 = 130 n2 = 150 AppendixLO1
Economists theorize that the recent recession has affected men more than women because men are typically employed in industries that have been hit hardest by the recession, such as manufacturing and construction. Women, on the other hand, are typically employed in services such as health care and
A major challenge for retailers like Best Buy is “showrooming”which describes customers who browse through their stores and then make their purchase from an online competitor. In an effort to measure the volume of showrooming, Best Buy observes the percentage of customers who leave their stores
People are considered obese when they are approximately 30 lbs over their healthy weight. Obesity can increase the risk of heart disease and diabetes, which could add to the cost of the health care system. Two random samples of adults were selected. The individuals in one of the samples lacked high
Office occupancy in a city is an indication of the economic health of the region in which it is located. A random sample of 165 offices in Boston was selected and it was found that 24 were vacant. A random sample of 145 offices in Chicago was selected and it was found that 17 were vacant.a.
Passing the ball between two players during a soccer game is a critical skill for the success of a team. A random sample of passes made by the English and German teams in a recent World Cup was drawn, and the number of successful passes in each sample was counted. The data are as follows:Germany
The federal government has become concerned about the default rates of loans made to students who attend for-profit schools. Two random samples of student loans were collected:one from students at for-profit schools and another from students at nonprofit schools. The following data show the sample
Baggage fees charged by airlines have received much attention recently as the industry has looked for ways to increase revenue without directly increasing fares. American Airlines would like to investigate if the average number of bags checked per flight fell after the company implemented fees for
A survey asked respondents how many online “friends”they have on networking sites such as Facebook. The following table presents the average number of friends for men and women along with the sample standard deviations and sample sizes. Assume the population variances for the number of friends
The recent financial crisis in Europe has resulted in high unemployment rates in some European Union countries. A recent survey of 120 adults from Greece found that 34 were currently unemployed. A corresponding survey of 135 adults from Spain found that 33 were currently unemployed.a. Perform a
McDonald’s would like to compare the wait times its drive-through customers experience vs. the wait times its customers using the restaurants’ inside counters experience.The following data represent the wait times, in minutes, randomly selected customers in the two types of groups experienced.
The on-time performances of flights in the airline industry are an important measurement that can help attract customers.The following data show the number of late flights from random samples taken from United Airlines and Southwest Airlines:United Southwest x1 = 130 x2 = 119 n1 = 175 n2 = 140a.
Pfizer would like to test the effectiveness of a new cholesterol medication it has recently developed. To test the effectiveness, the LDL cholesterol level of 12 randomly selected individuals was measured before and after they took the medication. The data are shown as follows and can be found in
The new health care plan that the federal government recently implemented has caused people to become concerned that a shortage of primary care physicians, particularly in under-served rural areas, will occur. Random samples of patient visits to primary care physicians in both rural and urban areas
The airline industry measures fuel efficiency by calculating how many miles one seat can travel, whether occupied or not, on one gallon of jet fuel. The following data show the fuel economy, in miles per seat, for 15 randomly selected flights on Delta and US Airways. These data can also be found in
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 gas mileage. Ten cars of this
In Major League Baseball, the umpire behind the plate uses his best judgment to decide if a pitch is within the strike zone or outside of the strike zone. The age-old question is whether the strike zone for the batter in the National League is different from the strike zone in the American League.
Brand loyalty in the automotive industry can be measured by the percentage of brand owners who purchase again. Suppose Cars.com would like to investigate if there is a difference in brand loyalty between Chevrolet and Buick owners.A random sample of 160 Chevrolet owners found that 68 had previously
According to the Institute for College Access & Success, the average student-loan debt for the most recent class of students from Pennsylvania is $9,000 more than the average for students in California. To test this claim, the following data were collected from random samples. Assume the population
The Excel file golf scores.xlsx contains a random sample of golf scores from two highly competitive sons of a certain statistics author. Each son claims he is the better golfer. Assume the population variances for each son’s golf score are equal.a. Perform a hypothesis test using a = 0.05 to
Consider the following ordered pairs:x 4 7 2 6 6 y 6 9 5 5 7 Calculate the sample correlation coefficient.AppendixLO1
Perform a hypothesis test with the data from Problem 14.1 to determine if the population correlation coefficient is not equal to zero using a = 0.05. What are your conclusions?AppendixLO1
Consider the following ordered pairs:x 7 6 2 3 y 6 8 9 6 Calculate the sample correlation coefficient.AppendixLO1
Perform a hypothesis test with the data from Problem 14.3 to determine if the population correlation coefficient is less than zero using a = 0.05. What are your conclusions?Applications AppendixLO1
Fair Isaac, the company that developed the credit score model used by most lenders today, would like to examine the linear relationship between the age and credit score of an individual. The following table shows the credit scores and ages of 10 randomly selected people:Age Credit Score Age Credit
Using the data from Problem 14.5 and a = 0.02, test if the population correlation coefficient between a person’s age and credit score is different than zero. What conclusions can you draw?AppendixLO1
Best Buy would like to investigate the linear relationship between the selling price of a Canon PowerShot digital camera and the demand for it. The following table shows the weekly demand for the camera in one particular market along with the corresponding price:Demand Price ($) Demand Price ($)16
Using a = 0.10 and the data from Problem 14.7, test if the population correlation coefficient between the selling price and the demand for the camera is less than zero.What conclusions can you draw?AppendixLO1
The University of Delaware would like to describe the linear relationship between the grade point average (GPA)and the starting monthly salary of a graduate who earned a business degree from the university. The following table shows the monthly starting salaries for eight graduates of the business
Using a = 0.05 and the data from Problem 14.9, test if the population correlation coefficient between the starting salary and the GPA of a University of Delaware business graduate is greater than zero. What conclusions can you draw?AppendixLO1
The following table shows the selling prices, in thousands of dollars, and the square footages of seven randomly selected houses recently sold by Century 21 Realtors.Price ($)Square Feet Price ($)Square Feet 258 2,730 249 2,310 191 1,860 245 2,450 253 2,140 282 2,920 168 2,180 Determine the sample
Using a = 0.10 and the data from Problem 14.11, test the significance of the population correlation coefficient between a house’s selling price and its square footage.What conclusions can you draw?AppendixLO1
Consider the following set of ordered pairs:x 4 7 2 6 6 y 6 9 5 5 7a. Calculate the slope and y-intercept for these data.b. Calculate the total sum of squares (SST).c. Partition the sum of squares into the SSR and SSE.AppendixLO1
Using the data from Problem 14.13, calculate the sample coefficient of determination and test the significance of the population coefficient of determination using a = 0.05.AppendixLO1
Consider the following set of ordered pairs:x 2 5 3 1 y 5 7 4 2a. Calculate the slope and y-intercept for these data.b. Calculate the SST.c. Partition the sum of squares into the SSR and SSE.AppendixLO1
Using the data from Problem 14.15, calculate the sample coefficient of determination and test the significance of the population coefficient of determination using a = 0.05.Applications AppendixLO1
The following table shows the hot dogs bought from a street vendor over the course of eight days (“Demand”). Also shown is the temperature for each day in degrees Celsius.Temperature(˚C) Demand Temperature(˚C) Demand 20 48 7 18 11 30 12 23 23 36 18 42 18 40 21 33a. Calculate the slope and
Use the data from Problem 14.17 to answer the following questions:a. Calculate the SST.b. Partition the total sum of squares into the SSR and SSE.c. Calculate the sample coefficient of determination.d. Test the significance of the population coefficient of determination using a = 0.05.AppendixLO1
Consider the following partially completed ANOVA summary table:Source df SS MS F Regression 1 600 Residual Total 9 1000a. Complete the remaining entries in the table.b. How many ordered pairs are in this sample?c. Calculate the sample coefficient of determination.d. Using a = 0.05, what conclusions
The following data set shows the entrance exam score(Verbal GMAT) for each of eight MBA students along with his or her grade point average (GPA) upon graduation.GMAT GPA GMAT GPA 310 3.7 350 4.0 290 3.0 270 3.0 260 3.1 300 3.7 280 3.2 300 3.0a. Calculate the slope and y-intercept for the linear
Use the data from Problem 14.20 to answer the following questions:a. Calculate the SST.b. Partition the SST into the SSR and SSE.c. Calculate the sample coefficient of determination.d. Test the significance of the population coefficient of determination using a = 0.05.AppendixLO1
Consider the following set of ordered pairs:x 3 6 2 4 4 y 5 6 4 6 2 Assuming that the regression equation is yn = 3.045 + 0.409x and the SSE = 9.727, construct a 95% confidence interval for x = 5.AppendixLO1
Using the data in Problem 14.22, construct a 95% prediction interval for x = 5.AppendixLO1
Consider the following set of ordered pairs:x 6 0 4 3 3 1 y 5 2 5 4 2 2 Assuming that the regression equation is yn = 1.679 +0.584x and the SSE = 3.547, construct a 90% confidence interval for x = 3.AppendixLO1
Using the data in Problem 14.24, construct a 90% prediction interval for x = 3.Applications AppendixLO1
As part of a research program for a new cholesterol drug, Johnson Pharmaceuticals would like to investigate the linear relationship between the ages and LDL (low-density lipoprotein) cholesterol levels of men. The following data set shows the ages and LDL cholesterol levels of seven randomly
Use the data in Problem 14.26 to construct a 95% prediction interval to estimate the LDL cholesterol level of a 30-year-old man. Verify your results with PHStat.AppendixLO1
Data in the Excel file points per game.xlsx show the number of wins eight teams had during a recent NFL season. Also in this file are the average points each team scored per game during the season.a. Construct a 90% confidence interval to estimate the average number of wins for teams that scored an
Use the data in Problem 14.28 to construct a 90% prediction interval estimating the number of wins a team that scores an average of 21 points a game will have. Verify your results using PHStat.AppendixLO1
Suppose the Department of Energy would like to investigate the linear relationship between the cost of heating a home during the month of February in the Northeast and the home’s square footage. Data for a random sample of 10 homes are as follows:Heating Cost ($)Square Footage Heating Cost
Use the data in Problem 14.30 to construct a 90% prediction interval to estimate the cost in February to heat a Northeast home that is 2,400 square feet. Verify your results using PHStat.AppendixLO1
Consider the following set of ordered pairs:x 3 6 2 4 4 y 5 8 4 6 5 Assuming that the regression equation is yn = 1.886 + 0.977x and that the SSE = 0.7955, test to determine if the slope is not equal to zero using a = 0.05.AppendixLO1
Using the data in Problem 14.32, construct a 95% confidence interval for the slope.AppendixLO1
Consider the following set of ordered pairs:x 6 0 4 3 3 1 y 5 2 5 4 5 6 Assuming that the regression equation is yn = 3.693 +0.285x and that the SSE = 7.650, test to determine if the slope is not equal to zero using a = 0.10.AppendixLO1
Using the data in Problem 14.34, construct a 90% confidence interval for the slope.Applications AppendixLO1
The Human Resource Department at Neumann University would like to examine the linear relationship between a faculty member’s performance rating (measured on a scale of 1–20) and his or her annual salary increase. The following table shows these data for eight randomly selected faculty members
Using the data in Problem 14.36, construct a 95% confidence interval for the regression slope.AppendixLO1
Wilmington University is concerned about the presence of grade inflation, which is defined as an increase in the average GPA of the institution’s students over time without a comparable increase in academic standards. To investigate this phenomenon, the average GPA for the student body was
Using the data in Problem 14.38, construct a 95% confidence interval for the regression slope.AppendixLO1
Suppose the Internet retailer Buy.com would like to investigate the linear relationship between the amount of time in minutes a purchaser spends on its Web site and the amount of money he or she spends on an order. The following table shows the data from a random sample of 12 customers and can also
Using the data in Problem 14.40, construct a 95% confidence interval for the regression slope.AppendixLO1
Consider the following set of ordered pairs:x 5 2 3 3 7 5 y 4 8 6 5 1 6a. Calculate the correlation coefficient.b. Using a = 0.05, perform a hypothesis test to determine if the population correlation coefficient is less than zero.AppendixLO1
Answer the following questions using the data from Problem 14.42:a. Calculate the slope and the y-intercept for the regression equation.b. Calculate the SST.c. Partition the SST into the SSR and the SSE.AppendixLO1
Answer the following questions using the data from Problem 14.42:a. Calculate the coefficient of determination.b. Using a = 0.05, test the significance of the population coefficient of determination.AppendixLO1
Answer the following questions using the data from Problem 14.42:a. Construct a 95% confidence interval for an average value of y given that x = 4.b. Construct a 95% prediction interval for y given that x = 4.AppendixLO1
Answer the following questions using the data from Problem 14.42:a. Using a = 0.05, test for the significance of the regression slope.b. Construct a 95% confidence interval for the population slope.Applications AppendixLO1
Suppose the Environmental Protection Agency (EPA)would like to investigate the linear relationship between the engine size of sedans and the miles per gallon (MPG)they get. Data from the Excel file engine size.xlsx show the engine size in cubic liters and rated miles per gallon for a selection of
Answer the following questions using the data from Problem 14.47: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 MPG of a 2.5-cubic liter engine.d. Construct
Answer the following questions using the data from Problem 14.47: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 engine size and MPG can be drawn from these results?AppendixLO1
Comcast’s customer service department asks its customers to rate their over-the-phone service on a scale of 1–20 immediately after their service has been completed. The company then matches each customer’s rating with the number of minutes the person waited on hold. The following table shows
Answer the following questions using the data from Problem 14.50:a. Calculate the coefficient of determination.b. Using a = 0.05, test the significance of the population coefficient of determination.c. Construct a 90% confidence interval for the average customer rating from customers who are on
Answer the following questions using the data from Problem 14.50: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 customer rating and time on hold can be drawn from these results?AppendixLO1
Suppose Consumer Reports would like to investigate the linear relationship between the battery life, in hours, and the screen size, in diagonal inches, of a laptop computer.The following table shows a random sample of eight laptops and the battery life and corresponding screen size of each. These
Answer the following questions using the data from Problem 14.53: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 battery life for a laptop with a 14-in.
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