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Introductory Statistics 8th Edition Prem S. Mann - Solutions

A television reporter is covering the election for mayor of a large city and will conduct an exit poll (interviews with voters immediately after they vote) to make an early prediction of the outcome. Assume that the eventual winner of the election will get 60% of the votes. a. What is the
A city is planning to build a hydroelectric power plant. A local newspaper found that 53% of the voters in this city favor the construction of this plant. Assume that this result holds true for the population of all voters in this city.a. What is the probability that more than 50% of the voters in
Refer to Exercise 6.93. Otto is trying out for the javelin throw to compete in the Olympics. The lengths of his javelin throws are normally distributed with a mean of 253 feet and a standard deviation of 8.4 feet. What is the probability that the total length of three of his throws will exceed 885
A certain elevator has a maximum legal carrying capacity of 6000 pounds. Suppose that the population of all people who ride this elevator have a mean weight of 160 pounds with a standard deviation of 25 pounds. If 35 of these people board the elevator, what is the probability that their combined
When is an estimator said to be consistent? Is the sample mean, x̅, a consistent estimator of µ? Explain.
A Census Bureau report revealed that 43.7% of Americans who moved between 2009 and 2010 did so for housing-related reasons, such as the desire to live in a new or better home or apartment (www.census.gov/newsroom/releases/archives/mobility_of_the_population/cb11-91.html). Suppose that this
Refer to the sampling distribution discussed in Section 7.1. Calculate and replace the sample means in Table 7.3 with the sample medians, and then calculate the average of these sample medians. Does this average of the medians equal the population mean? If yes, why does this make sense? If no, how
Suppose you want to calculate P(a < x̅ < b), where a and b are two numbers and x has a distribution with mean and standard deviation σ If a < µ < b (i.e., m lies in the interval a to b), what happens to the probability P(a < x̅ < b) as the sample size becomes larger?
Consider a large population with µ = 60 and σ = 10. Assuming n/N < .05, find the mean and standard deviation of the sample mean, , for a sample size ofa. 18b. 90
Consider a large population with µ = 90 and σ = 18. Assuming n/N < .05, find the mean and standard deviation of the sample mean, , for a sample size ofa. 10b. 3
A population of N = 5000 has σ = 25. In each of the following cases, which formula will you use to calculate σ and why? Using the appropriate formula, calculate σ for each of these cases.a. n = 300 b. n = 100
A population of N = 100,000 has σ = 40. In each of the following cases, which formula will you use to calculate σ and why? Using the appropriate formula, calculate σ for each of these cases.a. n = 2500b. n = 7000
For a population, µ = 125 and σ = 36.a. For a sample selected from this population, and Find the sample size. µ = 125 and σ = 3.6Assume n/N < .05.b. For a sample selected from this population, and Find the sample size. µ = 125 and σ = 2.25Assume n/N < .05.
For a population, µ = 46 and σ = 10.a. For a sample selected from this population, and Find the sample size. µ = 46 and σ = 2.0.Assume n/N < .05.b. For a sample selected from this population, and Find the sample size. µ = 46 and σ = 1.6.Assume n/N < .05.
According to the Project on Student Debt, the average student loan for college graduates of the class of 2010 was $25,000 (USA TODAY, April 24, 2012). Suppose that the student loans for all college graduates of the class of 2010 have a mean of $25,000 and a standard deviation of $6280. Let x̅ be
Explain briefly the meaning of sampling error. Give an example. Does such an error occur only in a sample survey, or can it occur in both a sample survey and a census?
The living spaces of all homes in a city have a mean of 2300 square feet and a standard deviation of 500 square feet. Let x̅ be the mean living space for a random sample of 25 homes selected from this city. Find the mean and standard deviation of the sampling distribution of x̅.
According to a report in The New York Times, bank tellers in the United States earn an average of $25,510 a year (Jessica Silver-Greenberg, The New York Times, April 22, 2012). Suppose that the current distribution of salaries of all bank tellers in the United States has a mean of $25,510 and a
According to the American Automobile Association’s 2012 annual report Your Driving Costs, the cost of owning and operating a four-wheel drive SUV is $11,350 per year (USA TODAY, April 27, 2012). This cost includes expenses for gasoline, maintenance, insurance, and financing for a vehicle that is
The standard deviation of the 2011 gross sales of all corporations is known to be $139.50 million. Let x̅ be the mean of the 2011 gross sales of a sample of corporations. What sample size will produce the standard deviation of equal to $15.50 million? Assume n/N < .05.
Consider the sampling distribution of given in Table 7.5.a. Calculate the value µ of using the formula µ = ˆ‘P(). Is the value of µ calculated in Exercise 7.6 the same as the value of µ calculated here?b. Calculate the value of Ïƒ by using the formulac. From Exercise 7.6, Ïƒ = 8.09.
Explain the central limit theorem.
The delivery times for all food orders at a fast-food restaurant during the lunch hour are normally distributed with a mean of 7.7 minutes and a standard deviation of 2.1 minutes. Let be the mean delivery time for a random sample of 16 orders at this restaurant. Calculate the mean and standard
Among college students who hold part-time jobs during the school year, the distribution of the time spent working per week is approximately normally distributed with a mean of 20.20 hours and a standard deviation of 2.60 hours. Let x̅ be the average time spent working per week for 18 randomly
The amounts of electricity bills for all households in a particular city have an approximately normal distribution with a mean of $140 and a standard deviation of $30. Let x̅ be the mean amount of electricity bills for a random sample of 25 households selected from this city. Find the mean and
The GPAs of all 5540 students enrolled at a university have an approximately normal distribution with a mean of 3.02 and a standard deviation of .29. Let x̅ be the mean GPA of a random sample of 48 students selected from this university. Find the mean and standard deviation of x̅, and comment on
The weights of all people living in a particular town have a distribution that is skewed to the right with a mean of 133 pounds and a standard deviation of 24 pounds. Let x̅ be the mean weight of a random sample of 45 persons selected from this town. Find the mean and standard deviation of x̅ and
According to an estimate, the average age at first marriage for men in the United States was 28.2 years in 2010 (Time, March 21, 2011). Suppose that currently the mean age for all U.S. men at the time of first marriage is 28.2 years with a standard deviation of 6 years and that this distribution is
Suppose that the incomes of all people in the United States who own hybrid (gas and electric) automobiles are normally distributed with a mean of $78,000 and a standard deviation of $8300. Let x̅ be the mean income of a random sample of 50 owners of such automobiles. Calculate the mean and
According to the American Time Use Survey, Americans watch television on weekdays for an average of 151 minutes per day (Time, July 11, 2011). Suppose that the current distribution of times spent watching television per weekday by all Americans has a mean of 151 minutes and a standard deviation of
Consider the following population of six numbers.a. Find the population mean.b. Liza selected one sample of four numbers from this population. The sample included the numbers 13, 8, 9, and 12. Calculate the sample mean and sampling error for this sample.c. Refer to part b. When Liza calculated the
If all possible samples of the same (large) size are selected from a population, what percentage of all the sample means will be within 2.5 standard deviations (σ) of the population mean?
If all possible samples of the same (large) size are selected from a population, what percentage of all the sample means will be within 1.5 standard deviations (σ) of the population mean?
For a population, N = 10,000, µ = 124, and σ = 18. Find the z value for each of the following forn = 36.a. x̅ = 128.60b. x̅ = 119.30c. x̅ = 116.88d. x̅ = 132.05
For a population, N = 205,000, µ = 66, and σ = 7. Find the z value for each of the following for n = 49.a. x̅ = 68.44b. x̅ = 58.75c. x̅ = 62.35d. x̅ = 71.82
Let x be a continuous random variable that has a normal distribution with µ = 75 and σ = 14. Assuming n/N < .05, find the probability that the sample mean, x̅, for a random sample of 20 taken from this population will bea. Between 68.5 and 77.3b. Less than 72.4
Let x be a continuous random variable that has a normal distribution with µ = 48 and σ = 8. Assuming n/N < .05, find the probability that the sample mean, , for a random sample of 16 taken from this population will bea. Between 49.6 and 52.2b. More than 45.7
Let x be a continuous random variable that has a distribution skewed to the right with µ = 60 and σ = 10. Assuming n/N < .05, find the probability that the sample mean, x̅, for a random sample of 40 taken from this population will bea. Less than 62.20b. Between 61.4 and 64.2
Let x be a continuous random variable that follows a distribution skewed to the left with µ = 90 and σ = 18. Assuming n/N < .05, find the probability that the sample mean, x̅, for a random sample of 64 taken from this population will bea. Less than 82.3b. Greater than 86.7
According to Moebs Services Inc., an individual checking account at U.S. community banks costs these banks between $175 and $200 per year (Time, November 21, 2011). Suppose that the average annual cost of all such checking accounts at U.S. community banks is $190 with a standard deviation of $20.
The GPAs of all students enrolled at a large university have an approximately normal distribution with a mean of 3.02 and a standard deviation of .29. Find the probability that the mean GPA of a random sample of 20 students selected from this university isa. 3.10 or higherb. 2.90 or lowerc. 2.95 to
Consider the following population of 10 numbers.a. Find the population mean.b. Rich selected one sample of nine numbers from this population. The sample included the numbers 20, 25, 13, 9, 15, 11, 7, 17, and 30. Calculate the sample mean and sampling error for this sample.c. Refer to part b. When
The delivery times for all food orders at a fast-food restaurant during the lunch hour are normally distributed with a mean of 7.7 minutes and a standard deviation of 2.1 minutes. Find the probability that the mean delivery time for a random sample of 16 such orders at this restaurant isa. Between
As mentioned in Exercise 7.22, according to the American Automobile Association’s 2012 annual report Your Driving Costs, the cost of owning and operating a four-wheel drive SUV is $11,350 per year (USA TODAY, April 27, 2012). Note that this cost includes expenses for gasoline, maintenance,
The times that college students spend studying per week have a distribution that is skewed to the right with a mean of 8.4 hours and a standard deviation of 2.7 hours. Find the probability that the mean time spent studying per week for a random sample of 45 students would bea. Between 8 and 9
The credit card debts of all college students have a distribution that is skewed to the right with a mean of $2840 and a standard deviation of $672. Find the probability that the mean credit card debt for a random sample of 36 college students would bea. Between $2600 and $2950b. Less than $3060
As mentioned in Exercise 7.39, according to the American Time Use Survey, Americans watch television each weekday for an average of 151 minutes (Time, July 11, 2011). Suppose that the current distribution of times spent watching television every weekday by all Americans has a mean of 151 minutes
The amounts of electricity bills for all households in a city have a skewed probability distribution with a mean of $140 and a standard deviation of $30. Find the probability that the mean amount of electric bills for a random sample of 75 households selected from this city will bea. Between $132
According to a PNC Financial Independence Survey released in March 2012, today’s U.S. adults in their 20s “hold an average debt of about $45,000, which includes everything from cars to credit cards to student loans to mortgages” (USA TODAY, April 24, 2012). Suppose that the current
As mentioned in Exercise 7.33, among college students who hold part-time jobs during the school year, the distribution of the time spent working per week is approximately normally distributed with a mean of 20.20 hours and a standard deviation of 2.60 hours. Find the probability that the average
Johnson Electronics Corporation makes electric tubes. It is known that the standard deviation of the lives of these tubes is 150 hours. The company’s research department takes a sample of 100 such tubes and finds that the mean life of these tubes is 2250 hours. What is the probability that this
A machine at Katz Steel Corporation makes 3-inch-long nails. The probability distribution of the lengths of these nails is normal with a mean of 3 inches and a standard deviation of .1 inch. The quality control inspector takes a sample of 25 nails once a week and calculates the mean length of these
Using the formulas of Section 5.3 of Chapter 5 for the mean and standard deviation of a discrete random variable, verify that the mean and standard deviation for the population probability distribution of Table 7.2 are 80.60 and 8.09, respectively.
The following data give the ages (in years) of all six members of a family.a. Let x denote the age of a member of this family. Write the population distribution of x.b. List all the possible samples of size four (without replacement) that can be selected from this population. Calculate the mean for
Consider a large population with p = .63. Assuming n/N < .05, find the mean and standard deviation of the sample proportion p̂ for a sample size ofa. 100b. 900
Consider a large population with p = .21. Assuming n/N < .05, find the mean and standard deviation of the sample proportion p̂ for a sample size ofa. 400b. 750
A population of N = 4000 has a population proportion equal to .12. In each of the following cases, which formula will you use to calculate σp̂ and why? Using the appropriate formula, calculate σp̂ for each of these cases.a. n = 800b. n = 30
A population of N = 1400 has a population proportion equal to .47. In each of the following cases, which formula will you use to calculate σp̂ and why? Using the appropriate formula, calculate σp̂ for each of these cases.a. n = 90b. n = 50
Indicate in which of the following cases the central limit theorem will apply to describe the sampling distribution of the sample proportion. a. n = 400 and p = .28 b. n = 80 and p = .05 c. n = 60 and p = .12 d. n = 100 and p = .035
Indicate in which of the following cases the central limit theorem will apply to describe the sampling distribution of the sample proportion. a. n = 20 and p = .45 b. n = 75 and p = .22 c. n = 350 and p = .01 d. n = 200 and p = .022
A company manufactured six television sets on a given day, and these TV sets were inspected for being good or defective. The results of the inspection follow.a. What proportion of these TV sets are good?b. How many total samples (without replacement) of size five can be selected from this
Investigation of all five major fires in a western desert during one of the recent summers found the following causes.a. What proportion of those fires were due to arson?b. How many total samples (without replacement) of size three can be selected from this population?c. List all the possible
Beginning in the second half of 2011, there were widespread protests in many American cities that were primarily against Wall Street corruption and the gap between the rich and the poor in America. According to a Time Magazine/ABT SRBI poll conducted by telephone during October 9–10, 2011, 86% of
The following data give the years of teaching experience for all five faculty members of a department at a university.a. Let x denote the years of teaching experience for a faculty member of this department. Write the population distribution of x.b. List all the possible samples of size three
According to a poll, 55% of Americans do not know that GOP stands for Grand Old Party (Time, October 17, 2011). Assume that this percentage is true for the current population of Americans. Let p̂ be the proportion in a random sample of 900 Americans who do not know that GOP stands for Grand Old
In a Time/Money Magazine poll of Americans age 18 years and older, 65% agreed with the statement, “We are less sure our children will achieve the American Dream” (Time, October 10, 2011). Assume that this result is true for the current population of Americans age 18 years and older. Let p̂ be
In a Time Magazine/Aspen poll of American adults conducted by the strategic research firm Penn Schoen Berland, these adults were asked, “In your opinion, what is more important for the U.S. to focus on in the next decade?” Eighty-three percent of the adults polled said domestic issues (Time,
If all possible samples of the same (large) size are selected from a population, what percentage of all sample proportions will be within 2.0 standard deviations (σp̂) of the population proportion?
If all possible samples of the same (large) size are selected from a population, what percentage of all sample proportions will be within 3.0 standard deviations (σp̂) of the population proportion?
For a population, N = 30,000 and p = .59. Find the z value for each of the following for n = 100. a. p̂ = .56 b. p̂ = .68 c. p̂ = .53 d. p̂ = .65
For a population, N = 18,000 and p = .25. Find the z value for each of the following for n = 70. a. p̂ = .26 b. p̂ = .32 c. p̂ = .17 d. p̂ = .20
Refer to Exercise 7.79. Beginning in the second half of 2011, there were widespread protests in many American cities that were primarily against Wall Street corruption and the gap between the rich and the poor in America. According to a Time Magazine/ABT SRBI poll conducted by telephone during
A survey of all medium- and large-sized corporations showed that 64% of them offer retirement plans to their employees. Let p̂ be the proportion in a random sample of 50 such corporations that offer retirement plans to their employees. Find the probability that the value of p̂ will be a. Between
According to a poll, 55% of Americans do not know that GOP stands for Grand Old Party (Time, October 17, 2011). Assume that this percentage is true for the current population of Americans. Let p̂ be the proportion in a random sample of 900 Americans who do not know that GOP stands for Grand Old
Let x̅ be the mean of a sample selected from a population.a. What is the mean of the sampling distribution of x̅ equal to?b. What is the standard deviation of the sampling distribution of x̅ equal to? Assume n/N < .05.
Dartmouth Distribution Warehouse makes deliveries of a large number of products to its customers. It is known that 85% of all the orders it receives from its customers are delivered on time. Let p̂ be the proportion of orders in a random sample of 100 that are delivered on time. Find the
Brooklyn Corporation manufactures DVDs. The machine that is used to make these DVDs is known to produce 6% defective DVDs. The quality control inspector selects a sample of 150 DVDs every week and inspects them for being good or defective. If 8% or more of the DVDs in the sample are defective, the
Mong Corporation makes auto batteries. The company claims that 80% of its LL70 batteries are good for 70 months or longer. Assume that this claim is true. Let p̂ be the proportion in a sample of 100 such batteries that are good for 70 months or longer. a. What is the probability that this sample
The package of Sylvania CFL 65-watt replacement bulbs that use only 16 watts claims that these bulbs have an average life of 8000 hours. Assume that the lives of all such bulbs have a normal distribution with a mean of 8000 hours and a standard deviation of 400 hours. Let be the average life of
A January 2010 article on money.cnn.com reported that the average monthly cable bill in the United States was $75. The article also stated that the annual percentage increase in the average monthly cable bill is 5% money.cnn.com/2010/01/06/news/companies/cable_bill_cost_increase/index.htm). Suppose
Refer to Exercise 7.93. The package of Sylvania CFL 65-watt replacement bulbs that use only 16 watts claims that these bulbs have an average life of 8000 hours. Assume that the lives of all such bulbs have a normal distribution with a mean of 8000 hours and a standard deviation of 400 hours. Find
Refer to Exercise 7.94. The current distribution of all monthly cable bills in the United States is approximately normal with a mean of $82.69 and a standard deviation of $11.17. Find the probability that the average monthly cable bill for 23 U.S. households with cable isa. Less than $80b. Between
The Toyota Prius hybrid car is estimated to get an average of 50 miles per gallon (mpg) of gas. However, the gas mileage varies from car to car due to a variety of conditions, driving styles, and other factors and has been reported to be as high as 70 mpg. Suppose that the distribution of miles per
A machine at Keats Corporation fills 64-ounce detergent jugs. The probability distribution of the amount of detergent in these jugs is normal with a mean of 64 ounces and a standard deviation of .4 ounce. The quality control inspector takes a sample of 16 jugs once a week and measures the amount of
In a large city, 88% of the cases of car burglar alarms that go off are false. Let p̂ be the proportion of false alarms in a random sample of 80 cases of car burglar alarms that go off in this city. Calculate the mean and standard deviation of p̂, and describe the shape of its sampling
Multiple choice questions:1. A sampling distribution is the probability distribution ofa. A population parameterb. A sample statisticc. Any random variable2. Non-sampling errors area. The errors that occur because the sample size is too large in relation to the population sizeb. The errors made
Briefly state and explain the central limit theorem.
The weights of all students at a large university have an approximately normal distribution with a mean of 145 pounds and a standard deviation of 18 pounds. Let be the mean weight of a random sample of certain students selected from this university. Calculate the mean and standard deviation of and
According to an estimate, the average price of homes in Martha’s Vineyard, Massachusetts, was $650,000 in 2011 (USA Today, August 11, 2011). Suppose that the current population distribution of home prices in Martha’s Vineyard has a mean of $650,000 and a standard deviation of $140,000, but the
Refer to Problem 15 above. The current population distribution of home prices in Martha’s Vineyard has a mean of $650,000 and a standard deviation of $140,000, but the shape of this distribution is unknown. Find the probability that the average price of a random sample of 100 homes selected from
At Jen and Perry Ice Cream Company, the machine that fills one-pound cartons of Top Flavor ice cream is set to dispense 16 ounces of ice cream into every carton. However, some cartons contain slightly less than and some contain slightly more than 16 ounces of ice cream. The amounts of ice cream in
In a September 2011 CNN/ORC International Poll, 15% of Americans said that they trust the (Federal) Government in Washington to do what is right always or most of the time (http://caffertyfile.blogs.cnn.com/2011/09/28/our-government is more badly divided than maybe it has ever been whats the
In a Time Magazine/Aspen Ideas Festival poll conducted by Penn Schoen Berland during June 1–8, 2011, Americans age 18 years and older were asked, “Overall, do you think the past decade has been one of progress or decline for the U.S. as a country?” Of the respondents, 68% said decline (Time,
Find z for each of the following confidence levels.a. 90%b. 95%c. 96%d. 97%e. 98%f. 99%
York Steel Corporation produces iron rings that are supplied to other companies. These rings are supposed to have a diameter of 24 inches. The machine that makes these rings does not produce each ring with a diameter of exactly 24 inches. The diameter of each of the rings varies slightly. It is
Yunan Corporation produces bolts that are supplied to other companies. These bolts are supposed to be 4 inches long. The machine that makes these bolts does not produce each bolt exactly 4 inches long. It is known that when the machine is working properly, the mean length of the bolts made on this
A hospital administration wants to estimate the mean time spent by patients waiting for treatment at the emergency room. The waiting times (in minutes) recorded for a random sample of 35 such patients are given below. The population standard deviation is not known.Construct a 99% confidence
A local gasoline dealership in a small town wants to estimate the average amount of gasoline that people in that town use in a 1-week period. The dealer asked 44 randomly selected customers to keep a diary of their gasoline usage, and this information produced the following data on gas used (in
A random sample of 25 life insurance policyholders showed that the average premium they pay on their life insurance policies is $685 per year with a standard deviation of $74. Assuming that the life insurance policy premiums for all life insurance policyholders have a normal distribution, make a
A drug that provides relief from headaches was tried on 18 randomly selected patients. The experiment showed that the mean time to get relief from headaches for these patients after taking this drug was 24 minutes with a standard deviation of 4.5 minutes. Assuming that the time taken to get relief

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