The Red Lobster restaurant chain regularly surveys its customers. On the basis of these surveys, the management of the chain claims that 75% of its customers rate the food as excellent. A consumer testing service wants to examine the claim by asking 460 customers to rate the food. What is the probability that less than 70% rate the food as excellent?
> The rising cost of electricity is a concern for homeowners. An economist wanted to determine how much electricity has increased over the past 5 years. A survey was conducted with the percentage increase recorded. Assuming that the population standard dev
> A survey of 80 randomly selected companies asked them to report the annual income of their presidents. Assuming that incomes are normally distributed with a standard deviation of $30,000, determine the 90% confidence interval estimate of the mean annual
> One measure of physical fitness is the amount of time it takes for the pulse rate to return to normal after exercise. A random sample of 100 women age 40 to 50 exercised on stationary bicycles for 30 minutes. The amount of time it took for their pulse ra
> The image of the Japanese manager is that of a workaholic with little or no leisure time. In a survey, a random sample of 250 Japanese middle managers was asked how many hours per week they spent in leisure activities (e.g., sports, movies, television).
> Draw a sampling distribution of a biased estimator.
> A time study of a large production facility was undertaken to determine the mean time required to assemble a cell phone. A random sample of the times to assemble 50 cell phones was recorded. An analysis of the assembly times reveals that they are normall
> As part of a project to develop better lawn fertilizers, a research chemist wanted to determine the mean weekly growth rate of Kentucky bluegrass, a common type of grass. A sample of 250 blades of grass was measured, and the amount of growth in 1 week wa
> A statistics professor is in the process of investigating how many classes university students miss each semester. To help answer this question, she took a random sample of 100 university students and asked each to report how many classes he or she had m
> In an article about disinflation, various investments were examined. The investments included stocks, bonds, and real estate. Suppose that a random sample of 200 rates of return on real estate investments was computed and recorded. Assuming that the stan
> In a survey conducted to determine, among other things, the cost of vacations, 64 individuals were randomly sampled. Each person was asked to compute the cost of her or his most recent vacation. Assuming that the standard deviation is $400, estimate with
> A survey of 400 statistics professors was undertaken. Each professor was asked how much time was devoted to teaching graphical techniques. We believe that the times are normally distributed with a standard deviation of 30 minutes. Estimate the population
> Because of different sales ability, experience, and devotion, the incomes of real estate agents vary considerably. Suppose that in a large city the annual income is normally distributed with a standard deviation of $15,000. A random sample of 16 real est
> One of the few negative side effects of quitting smoking is weight gain. Suppose that the weight gain in the 12 months following a cessation in smoking is normally distributed with a standard deviation of 6 pounds. To estimate the mean weight gain, a ran
> Suppose that the amount of time teenagers spend weekly working at part-time jobs is normally distributed with a standard deviation of 40 minutes. A random sample of 15 teenagers was drawn, and each reported the amount of time spent at part-time jobs (in
> It is known that the amount of time needed to change the oil on a car is normally distributed with a standard deviation of 5 minutes. The amount of time to complete a random sample of 10 oil changes was recorded and listed here. Compute the 99% confidenc
> Draw a sampling distribution of an unbiased estimator.
> The number of cars sold annually by used car salespeople is normally distributed with a standard deviation of 15. A random sample of 15 salespeople was taken, and the number of cars each sold is listed here. Find the 95% confidence interval estimate of t
> Among the most exciting aspects of a university professor’s life are the departmental meetings where such critical issues as the color of the walls will be painted and who gets a new desk are decided. A sample of 20 professors was asked
> How many rounds of golf do physicians (who play golf) play per year? A survey of 12 physicians revealed the following numbers: 3 41 17 1 33 37 18 15 17 12 29 51 Estimate with 95% confidence the mean number of rounds per year played by physicians, assumin
> The following observations are the ages of a random sample of 8 men in a bar. It is known that the ages are normally distributed with a standard deviation of 10. Determine the 95% confidence interval estimate of the population mean. Interpret the interva
> The following data represent a random sample of 9 marks (out of 10) on a statistics quiz. The marks are normally distributed with a standard deviation of 2. Estimate the population mean with 90% confidence. 7 9 7 5 4 8 3 10 9
> a. Given the following information, determine the 90% confidence interval estimate of the population mean using the sample median. Sample median = 500, = 12, and n = 50 b. Compare your answer in part (a) to that produced in part (c) of Exercise 10.16.
> Show that the sample mean is relatively more efficient than the sample median when estimating the population mean.
> Is the sample median a consistent estimator of the population mean? Explain.
> Is the sample median an unbiased estimator of the population mean? Explain.
> a. A random sample of 100 observations was randomly drawn from a population with a standard deviation of 5. The sample mean was calculated as x = 400. Estimate the population mean with 99% confidence. b. Repeat part (a) with x = 200. c. Repeat part (a) w
> Define unbiasedness.
> a. From the information given here determine the 95% confidence interval estimate of the population mean. x = 100 = 20 n = 25 b. Repeat part (a) with x = 200. c. Repeat part (a) with x = 500. d. Describe what happens to the width of the confidence inte
> a. A statistics practitioner randomly sampled 100 observations from a population with a standard deviation of 5 and found that x is 10. Estimate the population mean with 90% confidence. b. Repeat part (a) with a sample size of 25. c. Repeat part (a) with
> a. The mean of a sample of 25 was calculated as x = 500. The sample was randomly drawn from a population with a standard deviation of 15. Estimate the population mean with 99% confidence. b. Repeat part (a) changing the population standard deviation to 3
> a. Given the following information, determine the 98% confidence interval estimate of the population mean: x = 500 = 12 n = 50 b. Repeat part (a) using a 95% confidence level. c. Repeat part (a) using a 90% confidence level. d. Review parts (a)–(c) and
> a. A random sample of 25 was drawn from a normal distribution with a standard deviation of 5. The sample mean is 80. Determine the 95% confidence interval estimate of the population mean. b. Repeat part (a) with a sample size of 100. c. Repeat part (a) w
> a. The mean of a random sample of 25 observations from a normal population with a standard deviation of 50 is 200. Estimate the population mean with 95% confidence. b. Repeat part (a) changing the population standard deviation to 25. c. Repeat part (a) c
> a. A statistics practitioner took a random sample of 50 observations from a population with a standard deviation of 25 and computed the sample mean to be 100. Estimate the population mean with 90% confidence. b. Repeat part (a) using a 95% confidence lev
> Refer to Exercises 9.9–9.11. What do the probabilities tell you about the variances of X and X? Data from Exercise 9.9: Let X represent the result of the toss of a fair die. Find the following probabilities. Data from Exercise 9.11: An experiment consi
> An experiment consists of tossing five balanced dice. Find the following probabilities. (Determine the exact probabilities as we did in Tables 9.1 and 9.2 for two dice.) a. P(X = 1) b. P(X = 6) Data from Table 9.1: Data from Table 9.2: TABLE 9.1 Al
> Let X represent the mean of the toss of two fair dice. Use the probabilities listed in Table 9.2 to determine the following probabilities. a. P(X = 1) b. P(X = 6) Data from Table 9.2: TABLE 9.2 Sampling Distribution of X P(X) 1.0 1/36 1.5 2/36 2.0 3
> How do point estimators and interval estimators differ?
> Refer to Exercise 8.6. The professor would like to track (and possibly help) students who are in the top 10% of completion times. What completion time should he use? Data from Exercise 8.6: The amount of time it takes for a student to complete a statist
> Refer to Exercise 8.6. The professor wants to reward (with bonus marks) students who are in the lowest quarter of completion times. What completion time should he use for the cutoff for awarding bonus marks? Data from Exercise 8.6: The amount of time it
> Repeat Exercise 9.61 with samples of size 50. Data from Exercise 9.61: Independent random samples of 10 observations each are drawn from normal populations. The parameters of these populations are Population 1: μ = 280, σ = 25 Population 2: μ = 270, σ =
> Independent random samples of 10 observations each are drawn from normal populations. The parameters of these populations are Population 1: μ = 280, σ = 25 Population 2: μ = 270, σ = 30 Find the probability that the mean of sample 1 is greater than the m
> Repeat Exercise 9.59 for the worst umpire. Data from Exercise 9.59: Most televised baseball games display a pitch tracker that shows whether the pitch was in the strike zone, which in turn shows whether the umpire made the correct call. Major League Bas
> The amount of time it takes for a student to complete a statistics quiz is uniformly distributed between 30 and 60 minutes. One student is selected at random. Find the probability of the following events. a. The student requires more than 55 minutes to c
> Most televised baseball games display a pitch tracker that shows whether the pitch was in the strike zone, which in turn shows whether the umpire made the correct call. Major League Baseball keeps track of how well each umpire calls games. Batters swing
> In a Gallup survey, Americans were asked about their main source of news about current events around the world. If 20% of the population report that their main source is television news, find the probability that in a sample of 500 at least 22% say that
> In 2014, approximately 13% of nonelderly Americans adults had no health insurance. Suppose that a random sample of 400 such individuals was drawn. What is the probability that 15% or more had no health insurance?
> Refer to Exercise 9.55. A survey of a random sample of 1,200 undergraduate business students indicates that 336 students plan to major in accounting. What does this tell you about the professor’s claim? Data from Exercise 9.55: An accounting professor c
> An accounting professor claims that no more than one-quarter of undergraduate business students will major in accounting. What is the probability that in a random sample of 1,200 undergraduate business students, 336 or more will major in accounting?
> A psychologist believes that 80% of male drivers when lost continue to drive hoping to find the location they seek rather than ask directions. To examine this belief, he took a random sample of 350 male drivers and asked each what they did when lost. If
> A university bookstore claims that 50% of its customers are satisfied with the service and prices. a. If this claim is true, what is the probability that in a random sample of 600 customers less than 45% are satisfied? b. Suppose that in a random sample
> The Laurier Company’s brand has a market share of 30%. Suppose that 1,000 consumers of the product are asked in a survey which brand they prefer. What is the probability that more than 32% of the respondents say they prefer the Laurier brand?
> A commercial for a manufacturer of household appliances claims that 3% of all its products require a service call in the first year. A consumer protection association wants to check the claim by surveying 400 households that recently purchased one of the
> A uniformly distributed random variable has minimum and maximum values of 20 and 60, respectively. a. Draw the density function. b. Determine P(35 < X < 45). c. Draw the density function including the calculation of the probability in part (b).
> The manager of a restaurant in a commercial building has determined that the proportion of customers who drink tea is 14%. What is the probability that in the next 100 customers at least 10% will be tea drinkers?
> a. The manufacturer of aspirin claims that the proportion of headache sufferers who get relief with just two aspirins is 53%. What is the probability that in a random sample of 400 headache sufferers, less than 50% obtain relief? If 50% of the sample act
> The assembly line that produces an electronic component of a missile system has historically resulted in a 2% defective rate. A random sample of 800 components is drawn. What is the probability that the defective rate is greater than 4%? Suppose that in
> The proportion of eligible voters in the next election who will vote for the incumbent is assumed to be 55%. What is the probability that in a random sample of 500 voters less than 49% say they will vote for the incumbent?
> A binomial experiment where p = .4 is conducted. Find the probability that in a sample of 60 the proportion of successes exceeds .35.
> Determine the probability that in a sample of 100 the sample proportion is less than .75 if p = .80.
> a. The probability of success on any trial of a binomial experiment is 25%. Find the probability that the proportion of successes in a sample of 500 is less than 22%. b. Repeat part (a) with n = 800. c. Repeat part (a) with n = 1,000.
> a. In a binomial experiment with n = 300 and p = .5, find the probability that P^ is greater than 60%. b. Repeat part (a) with p = .55. c. Repeat part (a) with p = .6
> Xis normally distributed with mean 50 and standard deviation 8. What value of X is such that only 8% of values are below it?
> The property tax paid by homeowners in a large city was determined to be normally distributed with a mean of $2,800 and a standard deviation of $400. A random sample of four homes was drawn. a. What is the probability distribution of the mean of the samp
> A random variable is uniformly distributed between 100 and 150. a. Draw the density function. b. Find P(X > 110). c. Find P(120 < X < 135). d. Find P(X < 122).
> The number of pages produced by a fax machine in a busy office is normally distributed with a mean of 275 and a standard deviation of 75. Determine the probability that in 1 week (5 days) more than 1,500 faxes will be received?
> The restaurant in a large commercial building provides coffee for the occupants in the building. The restaurateur has determined that the mean number of cups of coffee consumed in a day by all the occupants is 2.0 with a standard deviation of .6. A new t
> Refer to Exercise 9.36. Does your answer change if you discover that the times needed to mark a midterm test are not normally distributed? Data from Exercise 9.36: The time it takes for a statistics professor to mark his midterm test is normally distrib
> The time it takes for a statistics professor to mark his midterm test is normally distributed with a mean of 4.8 minutes and a standard deviation of 1.3 minutes. There are 60 students in the professor’s class. What is the probability that he needs more t
> Refer to Exercise 9.34. Suppose that the professor discovers that the weights of people who use the elevator are normally distributed with an average of 75 kilograms and a standard deviation of 10 kilograms. Calculate the probability that the professor s
> The sign on the elevator in an office tower states, “Maximum Capacity 1,140 kilograms (2,500 pounds) or 16 Persons.” A professor of statistics wonders what the probability is that 16 persons would weigh more than 1,140 kilograms. Discuss what the profess
> The number of customers who enter a supermarket each hour is normally distributed with a mean of 600 and a standard deviation of 200. The supermarket is open 16 hours per day. What is the probability that the total number of customers who enter the super
> The manufacturer of cans of salmon that are supposed to have a net weight of 6 ounces tells you that the net weight is actually a normal random variable with a mean of 6.05 ounces and a standard deviation of .18 ounces. Suppose that you draw a random sam
> The amount of time spent by North American adults watching television per day is normally distributed with a mean of 6 hours and a standard deviation of 1.5 hours. a. What is the probability that a randomly selected North American adult watches televisio
> The marks on a statistics midterm test are normally distributed with a mean of 78 and a standard deviation of 6. a. What proportion of the class has a midterm mark of less than 75? b. What is the probability that a class of 50 has an average midterm mark
> Refer to Example 3.3. From the histogram of the marks, estimate the following probabilities. a. P(55 b. P(X > 65) c. P(X d. P(75 Data from Example 3.3: 30 25 20 15 10 Б 50 60 70 80 90 100 Marks LO Asuenbey
> The number of pizzas consumed per month by university students is normally distributed with a mean of 10 and a standard deviation of 3. a. What proportion of students consume more than 12 pizzas per month? b. What is the probability that in a random samp
> The amount of time the university professors devote to their jobs per week is normally distributed with a mean of 52 hours and a standard deviation of 6 hours. a. What is the probability that a professor works for more than 60 hours per week? b. Find the
> Refer to Exercise 9.26. Does your answer change if you discover that mortgages are not normally distributed? Data from Exercise 9.26: Statisticians determined that the mortgages of homeowners in a city is normally distributed with a mean of $250,000 and
> Statisticians determined that the mortgages of homeowners in a city is normally distributed with a mean of $250,000 and a standard deviation of $50,000. A random sample of 100 homeowners was drawn. What is the probability that the mean is greater than $2
> An automatic machine in a manufacturing process is operating properly if the lengths of an important subcomponent are normally distributed with mean = 117 cm and standard deviation = 5.2 cm. a. Find the probability that one selected subcomponent is longe
> Refer to Exercise 9.23. If the population of women’s heights is not normally distributed, which, if any, of the questions can you answer? Explain. Data from Exercise 9.23: The heights of North American women are normally distributed with a mean of 64 in
> The heights of North American women are normally distributed with a mean of 64 inches and a standard deviation of 2 inches. a. What is the probability that a randomly selected woman is taller than 66 inches? b. A random sample of four women is selected.
> a. Suppose that the standard deviation of a population with N = 10,000 members is 500. Determine the standard error of the sampling distribution of the mean when the sample size is 1,000. b. Repeat part (a) when n = 500. c. Repeat part (a) when n = 100.
> a. Calculate the finite population correction factor when the population size is N = 1,000 and the sample size is n = 100. b. Repeat part (a) when N = 3,000. c. Repeat part (a) when N = 5,000. d. What have you learned about the finite population correcti
> Repeat Exercise 9.18 for a standard deviation of 20. Data from Exercise 9.18: Given a normal population whose mean is 50 and whose standard deviation is 5, find the probability that a random sample of a. 4 has a mean between 49 and 52. b. 16 has a mean
> Refer to Example 3.2. Estimate the following from the histogram of the returns on investment B. a. P(X > 45) b. P(10 c. P(X d. P(35 Data from Example 3.2: Histogram of Returns on Investment B 18 16 14 12 10 -30 -15 0 15 30 45 60 75 Returns Aauen
> Repeat Exercise 9.18 for a standard deviation of 10. Data from Exercise 9.18: Given a normal population whose mean is 50 and whose standard deviation is 5, find the probability that a random sample of a. 4 has a mean between 49 and 52. b. 16 has a mean
> Given a normal population whose mean is 50 and whose standard deviation is 5, find the probability that a random sample of a. 4 has a mean between 49 and 52. b. 16 has a mean between 49 and 52. c. 25 has a mean between 49 and 52.
> Repeat Exercise 9.15 with n = 100. Data from Exercise 9.15: A sample of n = 16 observations is drawn from a normal population with μ = 1,000 and σ = 200. Find the following. a. P(X > 1,050) b. P(X < 960) c. P(X > 1,100)
> Unfortunately, robbery is an all-too frequent crime. Bank robberies tend to be the most lucrative for criminals. In most cases banks do not report the size of the loss. However, several researchers were able to gain access to bank robberies in England. H
> Several decades ago a large proportion of Americans smoked cigarettes. However, in recent years many adults have quit. To measure the extent of current smoking a random sample of American adults was asked to report whether they smoked (1 = yes, 2 = no).
> Wages and salaries make up only part of a total compensation. Other parts include paid leave, health insurance, and many others. In 2013, wages and salaries among manufacturers in the United States made up an average of 65.8% of total compensation. To de
> In 2015, there were 124,587,000 (Source: United States Census) households in the United States. There were 81,716,000 family households made up of married couples, single male, and single female households. To determine how many of each type a survey was
> Refer to Exercise 12.165. In 2006 the financial obligations ratio for renters was 23.65. Can we infer that financial obligations ratio for renters has increased between 2016 and this year? Data from Exercise 12.165: Another measure of indebtedness is th
> Refer to Exercise 12.164. Another measure of indebtedness is the financial obligations ratio, which adds automobile lease payments, rental on tenant occupied property, homeowner’s insurance, and property tax payments to the debt service ratio. In 2016, t
> In 2016, the average household debt service ratio for homeowners was 10.02. The household debt service ratio is the ratio of debt payments to disposable personal income. Debt payments consist of mortgage payments and payments on consumer debts. To determ
> Unfortunately, it is not uncommon for high school students in the United States to carry weapons (guns, knives, or clubs). To determine how prevalent this practice is, a survey of high school students was undertaken. Students were asked whether they carr
> Jim Cramer hosts CNBC’s “Mad Money” program. Mr. Cramer regularly makes suggestions about which stocks to buy and sell. How well has Mr. Cramer’s picks performed over the past two years (2005 to 2007)? To answer the question a random sample of Mr. Cramer
> The owner of a downtown parking lot suspects that the person he hired to run the lot is stealing some money. The receipts as provided by the employee indicate that the average number of cars parked in the lot is 125 per day and that, on average, each car
