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Statistics For Business And Economics 8th Edition Paul Newbold, William Carlson, Betty Thorne - Solutions

A random sample of 100 voters is taken to estimate the proportion of a state's electorate in favor of increasing the gasoline tax to provide additional revenue for highway repairs. What is the largest value that the standard error of the sample proportion in favor of this measure can take?
In the previous exercise, suppose that it is decided that a sample of 100 voters is too small to provide a sufficiently reliable estimate of the population proportion.It is required instead that the probability that the sample proportion differs from the population proportion (whatever its value)
Suppose that a mathematician said that it is impossible to obtain a simple random sample from a real-world population. Therefore, the whole basis for applying statistical procedures to real problems is useless. How would you respond?
A company wants to estimate the proportion of people who are likely to purchase electric shavers from those who watch the nationally telecast baseball playoffs. A random sample obtained information from 120 people who were identified as persons who watch baseball telecasts. Suppose that the
Suppose that 50% of all adult Americans believe that a major overhaul of the nation's health care delivery system is essential. What is the probability that more than 56% of a random sample of 150 adult Americans would hold this belief?
Suppose that 50% of all adult Americans believe that federal budget deficits at recent levels cause long-term harm to the nation's economy. What is the probability that more than 58% of a random sample of 250 adult Americans would hold this belief?
A journalist wanted to learn the views of the chief executive officers of the 500 largest U.S. corporations on program trading of stocks. In the time available, it was possible to contact only a random sample of 81 of these chief executive officers. If 55% of all the population members believe that
Forty percent of students at small colleges have brought their own personal computers to campus. A random sample of 120 entering freshmen was taken.a. What is the standard error of the sample proportion bringing their own personal computers to campus?b. What is the probability that the sample
An employee survey conducted two years ago by Rice Motors, Inc., found that 53% of its employees were concerned about future health care benefits. A random sample of 80 of these employees were asked if they were now concerned about future health care benefits. Answer the following, assuming that
The annual percentage salary increases for the chief executive officers of all midsize corporations are normally distributed with mean 12.2% and standard deviation 3.6%. A random sample of 81 of these chief executive officers was taken. What is the probability that more than half the sample members
A random sample of size n = 16 is obtained from a normally distributed population with a population mean of μ = 100 and a variance of σ2 = 25.a. What is the probability that x-bar > 101?b. What is the probability that the sample variance is greater than 45?c. What is the probability that the
A random sample of size n = 25 is obtained from a normally distributed population with a population mean of μ = 198 and a variance of σ2 = 100.a. What is the probability that the sample mean is greater than 200?b. What is the value of the sample variance such that 5% of the sample variances would
A random sample of size n = 18 is obtained from a normally distributed population with a population mean of μ = 46 and a variance of σ2 = 50.a. What is the probability that the sample mean is greater than 50?b. What is the value of the sample variance such that 5% of the sample variances would be
Given a population with a mean of μ = 100 and a variance of σ2 = 81, the central limit theorem applies when the sample size is n ≥ 25. A random sample of size n = 25 is obtained.a. What are the mean and variance of the sampling distribution for the sample means?b. What is the probability that
A process produces batches of a chemical whose impurity concentrations follow a normal distribution with a variance of 1.75. A random sample of 20 of these batches is chosen. Find the probability that the sample variance exceeds 3.10.
Monthly rates of return on the shares of a particular common stock are independent of one another and normally distributed with a standard deviation of 1.6. A sample of 12 months is taken.a. Find the probability that the sample standard deviation is less than 2.5.b. Find the probability that the
It is believed that first-year salaries for newly qualified accountants follow a normal distribution with a standard deviation of $2,500. A random sample of 16 observations was taken.a. Find the probability that the sample standard deviation is more than $3,000.b. Find the probability that the
A mathematics test of 100 multiple-choice questions is to be given to all freshmen entering a large university. Initially, in a pilot study the test was given to a random sample of 20 freshmen. Suppose that, for the population of all entering freshmen, the distribution of the number of correct
In a large city it was found that summer electricity bills for single-family homes followed a normal distribution with a standard deviation of $100. A random sample of 25 bills was taken.a. Find the probability that the sample standard deviation is less than $75.b. Find the probability that the
The number of hours spent watching television by students in the week before final exams has a normal distribution with a standard deviation of 4.5 hours. A random sample of 30 students was taken.a. Is the probability more than 0.95 that the sample standard deviation exceeds 3.5 hours?b. Is the
In Table 6.1 we considered the 15 possible samples of two observations from a population of N = 6 values of years on the job for employees. The population variance for these six values is as follows:σ = 47 / 12For each of the 15 possible samples, calculate the sample variance. Find the average of
A production process manufactures electronic components with timing signals whose duration follows a normal distribution. A random sample of six components was taken, and the durations of their timing signals were measured.a. The probability is 0.05 that the sample variance is greater than what
A random sample of 10 stock market mutual funds was taken. Suppose that rates of returns on the population of all stock market mutual funds follow a normal distribution.a. The probability is 0.10 that sample variance is greater than what percentage of the population variance?b. Find any pair of
Each member of a random sample of 15 business economists was asked to predict the rate of inflation for the coming year. Assume that the predictions for the whole population of business economists follow a normal distribution with standard deviation 1.8%.a. The probability is 0.01 that the sample
Given a population with a mean of μ = 100 and a variance of σ2 = 900, the central limit theorem applies when the sample size is n ≥ 25. A random sample of size n = 30 is obtained.a. What are the mean and variance of the sampling distribution for the sample means?b. What is the probability that
A precision instrument is checked by making 12 readings on the same quantity. The population distribution of readings is normal.a. The probability is 0.95 that the sample variance is more than what percentage of the population variance?b. The probability is 0.90 that the sample variance is more
A drug company produces pills containing an active ingredient. The company is concerned about the mean weight of this ingredient per pill, but it also requires that the variance (in squared milligrams) be no more than 1.5. A random sample of 20 pills is selected, and the sample variance is found to
A manufacturer has been purchasing raw materials from a supplier whose consignments have a variance of 15.4 (in squared pounds) in impurity levels. A rival supplier claims that she can supply consignments of this raw material with the same mean impurity level but with lower variance. For a random
What is meant by the statement that the sample mean has a sampling distribution?
An investor is considering six different money market funds. The average number of days to maturity for each of these funds is as follows:41, 39, 35, 35, 33, 38Two of these funds are to be chosen at random.a. How many possible samples of two funds are there?b. List all possible samples.c. Find the
The scores of all applicants taking an aptitude test required by a law school have a normal distribution with a mean of 420 and a standard deviation of 100. A random sample of 25 scores is taken.a. Find the probability that the sample mean score is higher than 450.b. Find the probability that the
A company services home air conditioners. It has been found that times for service calls follow a Normal distribution with a mean of 60 minutes and a standard deviation of 10 minutes. A random sample of four service calls was taken.a. What is the probability that the sample mean service time is
In a particular year, the percentage rates of return of U.S. common stock mutual funds had a normal distribution with a mean of 14.8 and a standard deviation of 6.3. A random sample of nine of these mutual funds was taken.a. What is the probability that the sample mean percentage rate of return
The lifetimes of a certain electronic component are known to be normally distributed with a mean of 1,600 hours and a standard deviation of 400 hours.a. For a random sample of 16 components, find the probability that the sample mean is more than 1,500 hours.b. For a random sample of 16 components,
Given a population with a mean of μ = 200 and a variance of σ2 = 625, the central limit theorem applies when the sample size n ≥ 25. A random sample of size n = 25 is obtained.a. What are the mean and variance of the sampling distribution for the sample mean?b. What is the probability that
Refer to the chapter appendix in order to derive the mean of the sampling distribution of the sample variances for a sample of n observations from a population of N members when the population variance is σ2. By appropriately modifying the argument regarding variances in the chapter appendix, show
It has been found that times taken by people to complete a particular tax form follow a normal distribution with a mean of 100 minutes and a standard deviation of 30 minutes. A random sample of nine people who have completed this tax form was taken.a. What is the probability that the sample mean
It was found that 80% of seniors at a particular college had accepted a job offer before graduation. For those accepting offers, salary distribution was normal with a mean of $37,000 and a standard deviation of $4,000. a. For a random sample of 60 seniors what is the probability that less than 70%
Plastic bags used for packaging produce are manufactured so that the breaking strengths of the bags are normally distributed with a standard deviation of 1.8 pounds per square inch. A random sample of 16 bags is selected.a. The probability is 0.01 that the sample standard deviation of breaking
A sample of 100 students is to be taken to determine which of two brands of beer is preferred in a blind taste test. Suppose that, in the whole population of students, 50% would prefer brand A.a. What is the probability that more than 60% of the sample members prefer brand A?b. What is the
Scores on a particular test, taken by a large group of students, follow a normal distribution with a standard deviation of 40 points. A random sample of 16 scores was taken to estimate the population mean score. Let the random variable x-bar denote the sample mean. What is the probability that the
In a particular year 40% of home sales were partially financed by the seller. A random sample of 250 sales is examined.a. The probability is 0.8 that the sample proportion is more than what amount?b. The probability is 0.9 that the sample proportion is less than what amount?c. The probability is
A candidate for office intends to campaign in a state if her initial support level exceeds 30% of the voters.A random sample of 300 voters is taken, and it is decided to campaign if the sample proportion supporting the candidate exceeds 0.28.a. What is the probability of a decision not to campaign
Given a population with mean μ = 400 and variance σ2 = 1, 600, the central limit theorem applies when the sample size is n ≥ 25. A random sample of size n = 35 is obtained.a. What are the mean and variance of the sampling distribution for the sample means?b. What is the probability that x-bar
It is known that the incomes of subscribers to a particular magazine have a normal distribution with a standard deviation of $6,600. A random sample of 25 subscribers is taken.a. What is the probability that the sample standard deviation of their incomes is more than $4,000?b. What is the
Batches of chemical are manufactured by a production process. Samples of 20 batches from a production run are selected for testing. If the standard deviation of the percentage of impurity contents in the sample batches exceeds 2.5%, the production process is thoroughly checked. Assume that the
A consumer product that has flourished in the last few years is bottled natural spring water. Jon Thorne is the CEO of a company that sells natural spring water. He has requested a report of the filling process of the 24-ounce (710-milliliter) bottles to be sure that they are being properly filled.
Prairie Flower Cereal, Inc., is a small but growing producer of hot and ready-to-eat breakfast cereals. The company was started in 1910 by Gordon Thorson, a successful grain farmer. You have been asked to test the cereal-packing process of 18-ounce (510-gram) boxes of sugar-coated wheat cereal. Two
Another product packaged by Prairie Flower Cereal, Inc., is an apple-cinnamon cereal. To test the packaging process of 40-ounce (1,134-gram) packages of this cereal, 23 samples of six packages each are randomly sampled and weighed. The lower and upper acceptance limits have been set at 1,120 grams
When a production process is operating correctly, the number of units produced per hour has a normal distribution with a mean of 92.0 and a standard deviation of 3.6. A random sample of 4 different hours was taken.a. Find the mean of the sampling distribution of the sample means.b. Find the
There is concern about the speed of automobiles traveling over a particular stretch of highway. For a random sample of 28 automobiles, radar indicated the following speeds, in miles per hour:a. Check for evidence of nonnormality.b. Find a point estimate of the population mean that is unbiased and
Assume a normal distribution with known population variance. Calculate the margin of error to estimate the population mean, m, for the following.a. 98% confidence level; n = 64; σ2 = 144b. 99% confidence level; n = 120; σ = 100
An automobile dealer has an inventory of 328 used cars. The mean mileage of these vehicles is to be estimated. Previous experience suggests that the population standard deviation is likely to be about 12,000 miles. If a 90% confidence interval for the population mean is to extend 2,000 miles on
A simple random sample is to be taken of 527 business majors in a college to estimate the proportion favoring greater emphasis on business ethics in the curriculum. How many observations are necessary to ensure that a 95% confidence interval for the population proportion extends at most 0.06 on
Show algebraically that Equation 7.23 is equal to Equation 7.24. That is,
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
Assume a normal distribution with known population variance. Calculate the width to estimate the population mean, m, for the following.a. 90% confidence level; n = 100; σ2 = 169b. 95% confidence level; n = 120; σ = 25
Assume a normal distribution with known population variance. Calculate the LCL and UCL for each of the following.a. x-bar = 50; n = 64; σ = 40; α = 0.05b. x-bar = 85; n = 225; σ2 = 400; α = 0.01c. x-bar = 510; n = 485; σ = 50; α = 0.10
A personnel manager has found that historically the scores on aptitude tests given to applicants for entry level positions follow a normal distribution with a standard deviation of 32.4 points. A random sample of nine test scores from the current group of applicants had a mean score of 187.9
It is known that the standard deviation in the volumes of 20-ounce (591-millliliter) bottles of natural spring water bottled by a particular company is 5 millliliters. One hundred bottles are randomly sampled and measured.a. Calculate the standard error of the mean.b. Find the margin of error of a
A college admissions officer for an MBA program has determined that historically applicants have undergraduate grade point averages that are normally distributed with standard deviation 0.45. From a random sample of 25 applications from the current year, the sample mean grade point average is
A process produces bags of refined sugar. The weights of the contents of these bags are normally distributed with standard deviation 1.2 ounces. The contents of a random sample of 25 bags had a mean weight of 19.8 ounces. Find the upper and lower confidence limits of a 99% confidence interval for
Find the standard error to estimate the population mean for each of the following.a. n = 17; 95% confidence level; s = 16b. n = 25; 90% confidence level; s2 = 43
Calculate the margin of error to estimate the population mean for each of the following.a. 99% confidence level; x1 = 25; x2 = 30; x3 = 33; x4 = 21b. 90% confidence level; x1 = 15; x2 = 17; x3 = 13; x4 = 11; x5 = 14
Twenty people in one large metropolitan area were asked to record the time (in minutes) that it takes them to drive to work. These times were as follows:30 42 35 40 45 22 32 15 41 4528 32 45 27 47 50 30 25 46 25a. Calculate the standard error.b. Find tv,α/2 for a 95% confidence interval for the
A random sample of eight homes in a particular suburb had the following selling prices (in thousands of dollars):192 183 312 227 309 396 402 390a. Check for evidence of nonnormality.b. Find a point estimate of the population mean that is unbiased and efficient.c. Use an unbiased estimation
Find the LCL and UCL for each of the following.a. α = 0.05; n = 25; x-bar = 560; s = 45b. α/2 = 0.05; n = 9; x-bar = 160; s2 = 36c. 1 - α = 0.98; n = 22; x-bar = 58; s = 15
A random sample of 16 tires was tested to estimate the average life of this type of tire under normal driving conditions. The sample mean and sample standard deviation were found to be 47,500 miles and 4,200 miles, respectively.a. Calculate the margin of error for a 95% confidence interval estimate
Calculate the width for each of the following.a. n = 6; s = 40; α = 0.05b. n = 22; s2 = 400; α = 0.01c. n = 25; s = 50; α = 0.10
In Example 7.5 we calculated a 95% confidence interval estimate of the Healthy Eating Index-2005 score for a random sample of participants at the time of their first interview. Recall that there are two observations for each person in the study. The first observation, identified by daycode = 1,
A machine that packages 18-ounce (510-gram) boxes of sugar-coated wheat cereal is being studied. The weights for a random sample of 100 boxes of cereal packaged by this machine are contained in the data file Sugar.a. Find a 90% confidence interval for the population mean cereal weight.b. Without
How much do students pay, on the average, for textbooks during the first semester of college? From a random sample of 400 students the mean cost was found to be $357.75, and the sample standard deviation was $37.89. Assuming that the population is normally distributed, find the margin of error of a
There is concern about the speed of automobiles traveling over a particular stretch of highway. For a random sample of 28 automobiles, radar indicated the following speeds, in miles per hour:Assuming a normal population distribution, find the margin of error of a 95% confidence interval for the
A clinic offers a weight-loss program. A review of its records found the following amounts of weight loss, in pounds, for a random sample of 24 of its clients at the conclusion of a 4-month program:a. Find a 99% confidence interval for the population mean.b. Without doing the calculations, explain
A business school placement director wants to estimate the mean annual salaries 5 years after students graduate. A random sample of 25 such graduates found a sample mean of $42,740 and a sample standard deviation of $4,780. Find a 90% confidence interval for the population mean, assuming that the
A car-rental company is interested in the amount of time its vehicles are out of operation for repair work. State all assumptions and find a 90% confidence interval for the mean number of days in a year that all vehicles in the company's fleet are out of operation if a random sample of nine cars
A random sample of 10 economists produced the following forecasts for percentage growth in real gross domestic product in the next year:2.2 2.8 3.0 2.5 2.4 2.6 2.5 2.4 2.7 2.6Use unbiased estimation procedures to find point estimates for the following:a. The population meanb. The population
Find the margin of error to estimate the population proportion for each of the following.a. n = 350; p` = 0.30; α = 0.01b. n = 275; p` = 0.45; α = 0.05c. n = 500; p` = 0.05; α = 0.10
Calculate the confidence interval to estimate the population proportion for each of the following.a. 98% confidence level; n = 450; p` = 0.10b. 95% confidence level; n = 240; p` = 0.01c. α = 0.04; n = 265; p` = 0.50
A small private university is planning to start a volunteer football program. A random sample of alumni is surveyed. It was found that 250 were in favor of this program, 75 were opposed, and 25 had no opinion.a. Estimate the percent of alumni in favor of this program. Let α = 0.05.b. Estimate the
Suppose that a random sample of 142 graduate-admissions personnel was asked what role scores on standardized tests (such as the GMAT or GRE) play in the consideration of a candidate for graduate school. Of these sample members, 87 answered "very important." Find a 95% confidence interval for the
In a random sample of 95 manufacturing firms, 67 indicated that their company attained ISO certification within the last two years. Find a 99% confidence interval for the population proportion of companies that have been certified within the last 2 years.
The Mendez Mortgage Company case study was given in Chapter 2. A random sample of n = 350 accounts of the company's total portfolio was selected. Estimate the proportion of all the company's accounts with an original purchase price of less than $10,000. The data is stored in the data file Mendez
Consider again the Mendez Mortgage Company case study in Chapter 2. From a random sample of n = 350 accounts of the company's total portfolio, estimate with 95% confidence the proportion of all the company's accounts in which the purchaser's latest FICO score was at least 750. The data is stored in
From a random sample of 400 registered voters in one city, 320 indicated that they would vote in favor of a proposed policy in an upcoming election.a. Calculate the LCL for a 98% confidence interval estimate for the population proportion in favor of this policy.b. Calculate the width of a 90%
Of a random sample of 250 marketing students, 180 rated a case of résumé inflation as unethical. Based on this information a statistician computed a confidence interval extending from 0.68 to 0.76 for the population proportion. What is the confidence level of this interval?
In a presidential election year, candidates want to know how voters in various parts of the country will vote.Suppose that 1 month before the election a random sample of 540 registered voters from one geographic region is surveyed. From this sample 320 indicate that they plan to vote for this
A random sample of 12 employees in a large manufacturing plant found the following figures for number of hours of overtime worked in the last month:22 16 28 12 18 36 23 11 41 29 26 31Use unbiased estimation procedures to find point estimates for the following:a. The population meanb. The population
Do you think that the government should bail out the automobile industry? Suppose that this question was asked in a recent survey of 460 Americans. Respondents were also asked to select the category corresponding to their age (younger than 30; 30 to 50; or older than 50). It was found that 140
It is important for airlines to follow the published scheduled departure times of flights. Suppose that one airline that recently sampled the records of 246 flights originating in Orlando found that 10 flights were delayed for severe weather, 4 flights were delayed for maintenance concerns, and all
Find the lower confidence limit for the population variance for each of the following normal populations.a. n = 21; a = 0.05; s2 = 16b. n = 16; a = 0.05; s = 8c. n = 28; a = 0.01; s = 15
Find the upper confidence limit for parts a–c of Exercise 7.42.In Exercise a. n = 21; a = 0.05; s2 = 16b. n = 16; a = 0.05; s = 8c. n = 28; a = 0.01; s = 15
Consider the following random sample from a normal population:12 16 8 10 9a. Find the 90% confidence interval for population variance.b. Find the 95% confidence interval for the population variance.
LDS wants to be sure that the leak rate (in cubic centimeters per second) of transmission oil coolers (TOCs) meets the established specification limits. A random sample 50 TOCs is tested, and the leak rates are recorded in the data file TOC. Estimate the variance in leak rate with a 95% confidence
A clinic offers a weight-loss program. A review of its records found the following amounts of weight loss, in pounds, for a random sample of 10 clients at the conclusion of the program: 18.2 25.9 6.3 11.8 15.4 20.3 16.8 18.5 12.3 17.2Find a 90% confidence interval for the population variance of
The quality-control manager of a chemical company randomly sampled twenty 100-pound bags of fertilizer to estimate the variance in the pounds of impurities. The sample variance was found to be 6.62. Find a 95% confidence interval for the population variance in the pounds of impurities.
A psychologist wants to estimate the variance of employee test scores. A random sample of 18 scores had a sample standard deviation of 10.4. Find a 90% confidence interval for the population variance. What are the assumptions, if any, to calculate this interval estimate?
A manufacturer is concerned about the variability of the levels of impurity contained in consignments of raw material from a supplier. A random sample of 15 consignments showed a standard deviation of 2.36 in the concentration of impurity levels. Assume normality.a. Find a 95% confidence interval
The Mendez Mortgage Company case study was introduced in Chapter 2. A random sample of n = 350 accounts of the company's total portfolio is stored in the data file Mendez Mortgage. Consider the variable "Original Purchase Price." Use unbiased estimation procedures to find point estimates of the
A manufacturer bonds a plastic coating to a metal surface. A random sample of nine observations on the thickness of this coating is taken from a week's output, and the thicknesses (in millimeters) of these observations are as follows:19.8 21.2 18.6 20.4 21.6 19.8 19.9 20.3 20.8Assuming normality,

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