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Statistics For Business And Economics 8th Edition Paul Newbold, William Carlson, Betty Thorne - Solutions
Assume simple random sampling. Calculate the variance of the sample mean, σ2x for each of the following.a. N = 1200; n = 80; s = 10b. N = 1425; n = 90; s2 = 64c. N = 3200; n = 200; s2 = 129
Assume simple random sampling. Calculate the 95% confidence interval estimate for the population mean for each of the following.a. N = 1200; n = 80; s = 10; x = 142b. N = 1425; n = 90; s2 = 64; x = 232.4c. N = 3200; n = 200; s2 = 129; x = 59.3
Assume simple random sampling. Calculate the confidence interval for the population total for each of the following.a. N = 1325; n = 121; s = 20; x = 182; 95% confidence levelb. N = 2100; n = 144; s = 50; x = 1,325; 98% confidence level
Assume simple random sampling. Calculate the confidence interval for the population proportion, P, for each of the following.a. N = 1058; n = 160; x = 40; 95% confidence levelb. N = 854; n = 81; x = 50; 99% confidence level
Take a random sample of 50 pages from this book and estimate the proportion of all pages that contain figures.
A firm employs 189 junior accountants. In a random sample of 50 of these, the mean number of hours overtime billed in a particular week was 9.7, and the sample standard deviation was 6.2 hours.a. Find a 95% confidence interval for the mean number of hours overtime billed per junior accountant in
An auditor, examining a total of 820 accounts receivable of a corporation, took a random sample of 60 of them. The sample mean was $127.43, and the sample standard deviation was $43.27.a. Using an unbiased estimation procedure, find an estimate of the population mean.b. Using an unbiased
On a particular day a consumer-advice bureau received 125 calls. For a random sample of 40 of these calls, it was found that mean time taken in providing the requested advice was 7.28 minutes, and the sample standard deviation was 5.32 minutes.a. Find a 99% confidence interval for the mean time
State whether each of the following statements is true or false. a. For a given number of population members and a given sample variance, the larger the number of sample members, the wider the 95% confidence interval for the population mean. b. For a given number of population members and a given
The demand for bottled water increases during the hurricane season in Florida. The operations manager at a plant that bottles drinking water wants to be sure that the filling process for 1-gallon bottles (1 gallon is approximately 3.785 liters) is operating properly.Currently, the company is
A senior manager, responsible for a group of 120 junior executives, is interested in the total amount of time per week spent by these people in internal meetings.A random sample of 35 of these executives was asked to keep diary records during the next week. When the results were analyzed, it was
A simple random sample of 400 from a total 1,395 colleges in the United States maintained that 39 colleges use the text Statistics Made Difficult and Boring. Find a 95% confidence interval for the proportion of all colleges using this text.
A business school dean is contemplating proposing a change in the requirements for graduation. At present, business majors are required to take one science course, chosen from a list of possible courses. The proposal is that this be replaced by the requirement that a course in ecology be taken. The
An accounting firm has 1200 clients. From a random sample of 120 clients, 110 indicated very high satisfaction with the firm's service. Find a 95% confidence interval for the proportion of all clients who are very highly satisfied with this firm.
A class has 420 students. The final examination is optional-taking it can raise, but cannot lower, a student's grade. Of a random sample of 80 students, 31 indicated that they would take the final examination.Find a 90% confidence interval for the total number of students in this class intending to
How large of a sample is needed to estimate the mean of a normally distributed population for each of the following?a. ME = 5; σ = 40; α = 0.01b. ME = 10; σ = 40; α = 0.01c. Compare and comment on your answers to parts a and b.
How large a sample is needed to estimate the population proportion for each of the following?a. ME = 0.03; α = 0.05b. ME = 0.05; α = 0.05c. Compare and comment on your answers to parts a and b.
How large a sample is needed to estimate the population proportion for each of the following?a. ME = 0.05; α = 0.01b. ME = 0.05; α = 0.10c. Compare and comment on your answers to parts a and b.
A research group wants to estimate the proportion of consumers who plan to buy a scanner for their PC during the next 3 months. a. How many people should be sampled so that the sampling error is at most 0.04 with a 90% confidence interval?b. What is the sample size required if the confidence is
A politician wants to estimate the proportion of constituents favoring a controversial piece of proposed legislation. Suppose that a 99% confidence interval that extends at most 0.05 on each side of the sample proportion is required. How many sample observations are needed?
Suppose that x1 and x2 are random samples of observations from a population with mean m and variance σ2. Consider the following three point estimators, X, Y, Z, of μ:a. Show that all three estimators are unbiased.b. Which of the estimators is the most efficient?c. Find the relative efficiency
The student government association at a university wants to estimate the percentage of the student body that supports a change being considered in the academic calendar of the university for the next academic year. How many students should be surveyed if a 90% confidence interval is desired and the
Determine the sample size needed for each of the following situations.a. N = 1,650 σ = 500 1.96σx-bar = 50b. N = 1,650 σ = 500 1.96σx-bar = 100c. N = 1,650 σ = 500 1.96σx-bar = 200d. Compare and comment on your answers to parts a through c.
Determine the sample size needed for each of the following situations.a. N = 3,300 σ = 500 1.96σx-bar = 50b. N = 4,950 σ = 500 1.96σx-bar = 50c. N = 5,000,000 σ = 500 1.96σx-bar = 50d. Compare and comment on your answers to parts a through c.
Determine the sample size for each of the following situations.a. N = 2,500 p` = 0.5 1.96spn = 0.05b. N = 2,500 p` = 0.5 1.96spn = 0.03c. Compare and comment on your answers to part a and part b.
The mean amount of the 812 mortgages taken out in a city in the past year must be estimated. Based on previous experience, a real estate broker knows that the population standard deviation is likely to be about $20,000. If a 95% confidence interval for the population mean is to extend $2,000 on
An automobile dealer has an inventory of 400 used cars. To estimate the mean mileage of this inventory, she intends to take a simple random sample of used cars. Previous studies suggest that the population standard deviation is 10,000 miles. A 90% confidence interval for the population mean must
A country club wants to poll a random sample of its 320 members to estimate the proportion likely to attend an early-season function. The number of sample observations should be sufficiently large to ensure that a 99% confidence interval for the population extends at most 0.05 on each side of the
An instructor in a class of 417 students is considering the possibility of a take-home final examination. She wants to take a random sample of class members to estimate the proportion who prefer this form of examination.If a 90% confidence interval for the population proportion must extend at most
Several drugs are used to treat diabetes. A sales specialist for a leading pharmaceutical company needs an estimate of the number of new prescriptions that were written during a particular month for his company€™s new diabetes drug. The numbers of new prescriptions in a random sample of 25
Suppose that Brent Matthews, manager of a Sam’s Club in Chattanooga, Tennessee, wants to estimate the mean number of gallons of milk that are sold during a typical weekday. Brent checks the sales records for a random sample of 16 days and finds the mean number of gallons sold is 150 gallons per
Find the reliability factor, zα/2, to estimate the mean, μ, of a normally distributed population with known population variance for the following.a. 93% confidence levelb. 96% confidence levelc. 80% confidence level
Everyone knows that exercise is important. Recently, employees of one large international corporation were surveyed and asked, How many minutes do you spend daily on some form of rigorous exercise? From a random sample of 25 employees, the \mean time spent on vigorous daily exercise was 28.5
The following data represent the number of passengers per flight for a random sample of 50 flights from Jacksonville, Florida, to Baltimore, Maryland, on one particular airline:Estimate the average number of passengers per flight with a 95% interval estimate.
The manager of a local fitness center wants an estimate of the number of times members use the weight room per month. From a random sample of 25 members the average number of visits to the weight room over the course of a month was 12.5 visits with a standard deviation of 3.8 visits. Assuming that
Eight randomly selected batches of a chemical were tested for impurity concentration. The percentage impurity levels found in this sample were as follows:3.2 4.3 2.1 2.8 3.2 3.6 4.0 3.8a. Find the most efficient estimates of the population mean and variance.b. Estimate the proportion of batches
A marketing research assistant for a veterinary hospital surveyed a random sample of 457 pet owners. Respondents were asked to indicate the number of times that they visit their veterinarian each year. The sample mean response was 3.59 and the sample standard deviation was 1.045. Based on these
A random sample of 174 college students was asked to indicate the number of hours per week that they surf the Internet for either personal information or material for a class assignment. The sample mean response was 6.06 hours and the sample standard deviation was 1.43 hours. Based on these
A sample of 33 accounting students recorded the number of hours that they spent studying for a final exam. The data are stored in the data file Study.a. Give an example of an unbiased, consistent, and efficient estimator of the population mean.b. Find the sampling error for a 95% confidence
Dr. Mihaela Sabou wants to estimate the average length of a hospital stay (number of days) for patients with a certain infectious disease. From a random sample of 25 patient records, she finds that the average number of days in the hospital for such patients is 6 days, with a standard deviation of
Suppose that a survey of race fans at this week’s Daytona 500 NASCAR race were asked, Is this your first time attending the Daytona 500? From a random sample of 250 race fans, 100 answered in the affirmative.a. Find the standard error to estimate the population proportion of first timers.b. Find
The following data represent the number of passengers per flight in a random sample of 20 flights from Vienna, Austria, to Cluj-Napoca, Romania, with a new airline:a. What is the reliability factor for a 90% confidence interval estimate of the mean number of passengers per flight?b. Find the LCL
Find the reliability factor, zα/2, to estimate the mean, m, of a normally distributed population with known population variance for the following.a. α = 0.08b. α/2 = 0.02
What is the most common method to renew vehicle registration? In checking a random sample of 500 motor vehicle renewal registrations in one county, the finance department found that 200 were mailed, 160 were paid in person at the county finance department office, and the remainder was paid online
Consider the data in Exercise 7.90. Suppose that we computed for the population proportion who pay for vehicle registration by mail a confidence interval extending from 0.34 to 0.46. What is the confidence level of this interval?
Consider the data in Exercise 7.90. It was reported in the local paper that less than one-third (from 23.7% to 32.3%) of the population prefers the online renewal process. What is the confidence level of this interval estimate?
The county finance department in Exercise 7.90 also wants information about renewals of disabled parking placards. Suppose that in a sample of 350 transactions for disabled parking placards, it was found that 250 were paid electronically.a. What is the margin of error for a 99% confidence interval
What is the typical age of a person who renews his or her driver’s license online? From a random sample of 460 driver’s license renewal transactions, the mean age was 42.6 and the standard deviation was 5.4. Compute the 98% confidence interval estimate of the mean age of online renewal users in
A test was taken by 90 students. A random sample of 10 scores found the following results:93 71 62 75 81 63 87 59 84 72a. Find a 90% confidence interval for the population’s mean score.b. Without doing the calculations, state whether a 95% confidence interval for the population mean would be
A corporation has 272 accounts receivable in a particular category. A random sample of 50 of them was taken. The sample mean was $492.36, and the sample standard deviation was $149.92.a. Find a 99% confidence interval for the population mean value of these accounts receivable.b. Find a 95%
A corporation employs 148 sales representatives. A random sample of 60 of them was taken, and it was found that, for 36 of the sample members, the volume of orders taken this month was higher than for the same month last year. Find a 95% confidence interval for the population proportion of sales
Several drugs are used to treat high blood pressure. A sales specialist for a leading pharmaceutical company randomly sampled the records of 10 sales districts to estimate the number of new prescriptions that had been written during a particular month for the company’s new blood pressure
The president’s policy on domestic affairs received a 45% approval rating in a recent poll. The margin of error was given as 0.035. What sample size was used for this poll if we assume a 95% confidence level?
A dependent random sample from two normally distributed populations gives the following results:n = 15 d-bar = 25.4 sd = 2.8a. Find the 95% confidence interval for the difference between the means of the two populations.b. Find the margin of error for a 95% confidence interval for the difference
Assuming unequal population variances, determine the number of degrees of freedom for each of the following:a. nx = 16 s2x = 5ny = 4 s2y = 36b. nx = 9 s2x = 30ny = 16 s2y = 4
Determine the margin of error for a 95% confidence interval for the difference between population means for each of the following (assume equal population variances):a. nx = 10 s2x = 6 x-bar = 200ny = 16 s2y = 10 y-bar = 160b. nx = 5 s2x = 6 x-bar = 200ny = 8 s2y = 10 y-bar = 160c. The sample sizes
A manufacturer knows that the numbers of items produced per hour by machine A and by machine B are normally distributed with a standard deviation of 8.4 items for machine A and a standard deviation of 11.3 items for machine B. The mean hourly amount produced by machine A for a random sample of 40
From a random sample of six students in an introductory finance class that uses group-learning techniques, the mean examination score was found to be 76.12 and the sample standard deviation was 2.53. For an independent random sample of nine students in another introductory finance class that does
Prairie Flower Cereal, Inc., is a small, but growing, producer of hot and ready-to-eat breakfast cereals. Gordon Thorson, a successful grain farmer, started the company in 1910 (Carlson 1997). Two machines are used for packaging 18-ounce (510-gram) boxes of sugar-coated wheat cereal. Estimate the
Recent business graduates currently employed in full-time positions were surveyed. Family backgrounds were self-classified as relatively high or low socioeconomic status. For a random sample of 16 high-socioeconomic-status recent business graduates, the mean total compensation was $34,500 and the
Suppose that for a random sample of 200 firms that revalued their fixed assets, the mean ratio of debt to tangible assets was 0.517 and the sample standard deviation was 0.148. For an independent random sample of 400 firms that did not revalue their fixed assets, the mean ratio of debt to tangible
A researcher intends to estimate the effect of a drug on the scores of human subjects performing a task of psychomotor coordination. The members of a random sample of 9 subjects were given the drug prior to testing.The mean score in this group was 9.78, and the sample variance was 17.64. An
Calculate the margin of error for each of the following:a. nx = 280 p`x = 0.75ny = 320 p`y = 0.68b. nx = 210 p`x = 0.51ny = 200 p`y = 0.48
Calculate the 95% confidence interval for the difference in population proportions for each of the following:a. nx = 350 p`x = 0.64ny = 300 p`y = 0.68b. nx = 245 p`x = 0.45ny = 230 p`y = 0.48
A confidence interval for the difference between the means of two normally distributed populations based on the following dependent samples is desired:Before After 6 ............ 812 ................148 ............ 910 ................136 ................. 7a. Find the margin of error for a 90%
In a random sample of 120 large retailers, 85 used regression as a method of forecasting. In an independent random sample of 163 small retailers, 78 used regression as a method of forecasting. Find a 98% confidence interval for the difference between the two population proportions.
Regulatory agencies and the U.S. Congress recognize both the values and emerging issues for small firms as the Sarbanes-Oxley Act of 2002 (SOX) is implemented. On April 23, 2006, the Advisory Committee on Smaller Public Companies issued a final report to the Security and Exchange Commission
Would you use the library more if the hours were extended? From a random sample of 138 freshmen, 80 indicated that they would use the school’s library more if the hours were extended. In an independent random sample of 96 sophomores, 73 responded that they would use the library more if the hours
A random sample of 100 men contained 61 in favor of a state constitutional amendment to retard the rate of growth of property taxes. An independent random sample of 100 women contained 54 in favor of this amendment. A confidence interval extending from 0.04 to 0.10 was calculated for the difference
Supermarket shoppers were observed and questioned immediately after putting an item in their cart. Of a random sample of 510 choosing a product at the regular price, 320 claimed to check the price before putting the item in their cart. Of an independent random sample of 332 choosing a product at a
Independent random samples from two normally distributed populations give the following results:nx = 15 x-bar = 400 sx = 20ny = 13 y-bar = 360 sy = 25Assume that the unknown population variances are equal and find a 90% confidence interval for the difference between population means.
Independent random samples from two normally distributed populations give the following results:nx = 15 x-bar = 400 sx = 10ny = 13 y-bar = 360 sy = 40If we do not assume that the unknown population variances are equal, what is the 90% confidence interval for the difference between population means?
Independent random samples from two normally distributed populations give the following results:nx = 10 x-bar = 480 sx = 30ny = 12 y-bar = 520 sy = 25a. If we assume that the unknown population variances are equal, find the 90% confidence interval for the difference of population means.b. If we do
A company sends a random sample of 16 of its salespeople to a course designed to increase their motivation and, hence, presumably their effectiveness. In the following year these people generated sales with an average value of $625,000 and a sample standard deviation of $80,000. During the same
A proposal for a new 1-cent tax increase to support cancer research is to appear on the ballot in one county's next election. The residents in two cities were questioned as to their level of support. In Sterling Heights a recent survey of 225 residents showed that 140 people supported the proposal,
An educational study was designed to investigate the effectiveness of a reading program of elementary age children. Each child was given a pretest and posttest. Higher posttest scores would indicate reading improvement. From a very large population, a random sample of scores for the pretest and
Is the average amount spent on textbooks per semester by accounting majors significantly different from the average amount spent on textbooks per semester by management majors? Answer this question with a 90% confidence interval using the following data from random samples of students majoring in
The supervisor of an orange juice-bottling company is considering the purchase of a new machine to bottle 16-fluid-ounce (473-milliliter) bottles of 100% pure orange juice and wants an estimate of the difference in the mean filling weights between the new machine and the old machine. Random samples
An agency offers students preparation courses for a graduate school admissions test. As part of an experiment to evaluate the merits of the course, 12 students were chosen and divided into six pairs in such a way that the two members of any pair had similar academic records. Before taking the test,
A newspaper article reported that 400 people in one state were surveyed and 75% were opposed to a recent court decision. The same article reported that a similar survey of 500 people in another state indicated opposition by only 45%. Construct a 95% confidence interval of the difference in
The Healthy Eating Index measures on a 100-point scale the adequacy of consumption of vegetables, fruits, grains, milk, meat and beans, and liquid oils. This scale is called HEI2005 (Guenther et al.2007). There are two interviews for each person in the study. The first interview is identified by
Consider again the data at the time of the first interview 1daycode = 12 for participants in the HEI-2005 study (Guenther et al. 2007). Find a 95% confidence interval estimate of the difference in the mean HEI-2005 scores between participants in the HEI study who smoke and those who do not smoke.
A random sample of 10 pairs of identical houses was chosen in a large Midwestern city, and a passive solar heating system was installed in one house from each pair. The total fuel bills (in dollars) for three winter months for these homes were then determined, as shown in the accompanying table.
A random sample of six salespeople who attended a motivational course on sales techniques was monitored 3 months before and 3 months after the course. The table shows the values of sales (in thousands of dollars) generated by these six salespeople in the two periods. Assume that the population
Independent random sampling from two normally distributed populations gives the following results:nx = 64; x-bar = 400; σx = 20ny = 36; y-bar = 360; σy = 25Find a 90% confidence interval estimate of the difference between the means of the two populations.
Independent random sampling from two normally distributed populations gives the following results:nx = 81; x-bar = 140; σ2x = 25ny = 100; y-bar = 120; σ2y = 14Find a 95% confidence interval estimate of the difference between the means of the two populations.
Assuming equal population variances, determine the number of degrees of freedom for each of the following:a. nx = 16 s2x = 30ny = 9 s2y = 36b. nx = 12 s2x = 30ny = 14 s2y = 36c. nx = 20 s2x = 16ny = 8 s2y = 25
Assuming equal population variances, compute the pooled sample variance s2p for part a through part c of Exercise 8.8.In exercisea. nx = 16 s2x = 30ny = 9 s2y = 36b. nx = 12 s2x = 30ny = 14 s2y = 36c. nx = 20 s2x = 16ny = 8 s2y = 25
A random sample of n = 25 is obtained from a population with variance σ2, and the sample mean is computed to be x-bar = 70. Consider the null hypothesis H0: μ = 80 versus the alternative hypothesis H1: μ < 80. Compute the p-value for the following options.a. The population variance is σ2 =
A manufacturer of detergent claims that the contents of boxes sold weigh on average at least 16 ounces. The distribution of weight is known to be normal, with a standard deviation of 0.4 ounce. A random sample of 16 boxes yielded a sample mean weight of 15.84 ounces. Test at the 10% significance
A company that receives shipments of batteries tests a random sample of nine of them before agreeing to take a shipment. The company is concerned that the true mean lifetime for all batteries in the shipment should be at least 50 hours. From past experience it is safe to conclude that the
A pharmaceutical manufacturer is concerned that the impurity concentration in pills should not exceed 3%. It is known that from a particular production run impurity concentrations follow a normal distribution with a standard deviation of 0.4%. A random sample of 64 pills from a production run was
Test the hypothesesH0: μ ≤ 100H1: μ > 100Using a random sample of n = 25, a probability of Type I error equal to 0.05, and the following sample statistics.a. x-bar = 106; s = 15b. x-bar = 104; s = 10c. x-bar = 95; s = 10d. x-bar = 92; s = 18
Test the hypothesesH0: μ = 100H1: μ < 100using a random sample of n = 36, a probability of Type I error equal to 0.05, and the following sample statistics.a. x-bar = 106; s = 15b. x-bar = 104; s = 10c. x-bar = 95; s = 10d. x-bar = 92; s = 18
An engineering research center claims that through the use of a new computer control system, automobiles should achieve, on average, an additional 3 miles per gallon of gas. A random sample of 100 automobiles was used to evaluate this product. The sample mean increase in miles per gallon achieved
A random sample of 1,562 undergraduates enrolled in management ethics courses was asked to respond on a scale from 1 (strongly disagree) to 7 (strongly agree) to this proposition: Senior corporate executives are interested in social justice. The sample mean response was 4.27, and the sample
You have been asked to evaluate single-employer plans after the establishment of the Health Benefit Guarantee Corporation. A random sample of 76 percentage changes in promised health benefits was observed. The sample mean percentage change was 0.078, and the sample standard deviation was 0.201.Find
A random sample of 172 marketing students was asked to rate, on a scale from 1 (not important) to 5 (extremely important), health benefits as a job characteristic. The sample mean rating was 3.31, and the sample standard deviation was 0.70. Test at the 1% significance level the null hypothesis that
A random sample of 170 people was provided with a forecasting problem. Each sample member was given, in two ways, the task of forecasting the next value of a retail sales variable. The previous 20 values were presented both as numbers and as points on a graph. Subjects were asked to predict the
The accounts of a corporation show that, on average, accounts payable are $125.32. An auditor checked a random sample of 16 of these accounts. The sample mean was $131.78 and the sample standard deviation was $25.41. Assume that the population distribution is normal. Test at the 5% significance
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