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Introductory Statistics 8th Edition Prem S. Mann - Solutions

It is said that happy and healthy workers are efficient and productive. A company that manufactures exercising machines wanted to know the percentage of large companies that provide on-site health club facilities. A sample of 240 such companies showed that 96 of them provide such facilities on
A mail-order company promises its customers that the products ordered will be mailed within 72 hours after an order is placed. The quality control department at the company checks from time to time to see if this promise is fulfilled. Recently the quality control department took a sample of 50
In a random sample of 50 homeowners selected from a large suburban area, 19 said that they had serious problems with excessive noise from their neighbors.a. Make a 99% confidence interval for the percentage of all homeowners in this suburban area who have such problems.b. Suppose the confidence
An Accountemps survey asked workers to identify what behavior of coworkers irritates them the most. Forty-one percent of the workers surveyed said that sloppy work is the most irritating behavior. Suppose that this percentage is based on a random sample of 500 workers.a. Construct a 95% confidence
In a Time/Money Magazine poll of Americans of 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 poll was based on a random sample of 1600 Americans. a. Construct a 95% confidence
A researcher wanted to know the percentage of judges who are in favor of the death penalty. He took a random sample of 15 judges and asked them whether or not they favor the death penalty. The responses of these judges are given here.a. What is the point estimate of the population proportion?b.
The management of a health insurance company wants to know the percentage of its policyholders who have tried alternative treatments (such as acupuncture, herbal therapy, etc.). A random sample of 24 of the company€™s policyholders was asked whether or not they have ever tried such treatments.
Tony’s Pizza guarantees all pizza deliveries within 30 minutes of the placement of orders. An agency wants to estimate the proportion of all pizzas that are delivered within 30 minutes by Tony’s. What is the most conservative estimate of the sample size that would limit the margin of error to
Refer to Exercise 8.92. Assume that a preliminary study has shown that 93% of all Tony’s pizzas are delivered within 30 minutes. How large should the sample size be so that the 99% confidence interval for the population proportion has a margin of error of .02?
A consumer agency wants to estimate the proportion of all drivers who wear seat belts while driving. Assume that a preliminary study has shown that 76% of drivers wear seat belts while driving. How large should the sample size be so that the 99% confidence interval for the population proportion has
Refer to Exercise 8.94. What is the most conservative estimate of the sample size that would limit the margin of error to within .03 of the population proportion for a 99% confidence interval?
You want to estimate the proportion of students at your college who hold off-campus (part-time or fulltime) jobs. Briefly explain how you will make such an estimate. Collect data from 40 students at your college on whether or not they hold off-campus jobs. Then calculate the proportion of students
You want to estimate the percentage of students at your college or university who are satisfied with the campus food services. Briefly explain how you will make such an estimate. Select a sample of 30 students and ask them whether or not they are satisfied with the campus food services. Then
Because of inadequate public school budgets and lack of money available to teachers for classroom materials, many teachers often use their own money to buy materials used in the classrooms. A random sample of 100 public school teachers selected from an eastern state showed that they spent an
A bank manager wants to know the mean amount owed on credit card accounts that become delinquent. A random sample of 100 delinquent credit card accounts taken by the manager produced a mean amount owed on these accounts equal to $2640. The population standard deviation was $578. a. What is the
Complete the following sentences using the terms population parameter and sample statistic. a. Estimation means assigning values to a ___________ based on the value of a ___________. b. An estimator is a ___________ used to estimate a ___________. c. The value of a ___________ is called the point
A company that makes toaster ovens has done extensive testing on the accuracy of its temperature setting mechanism. For a previous toaster model of this company, the standard deviation of the temperatures when the mechanism is set for 350oF is 5.78o. Assume that this is the population standard
A college registrar has received numerous complaints about the online registration procedure at her college, alleging that the system is slow, confusing, and error prone. She wants to estimate the proportion of all students at this college who are dissatisfied with the online registration
Refer to Problem 11. Assume that a preliminary study has shown that 70% of the students surveyed at this college are dissatisfied with the current online registration system. How large a sample should be taken in this case so that the margin of error is within .05 of the population proportion for a
Dr. Garcia estimated the mean stress score before a statistics test for a random sample of 25 students. She found the mean and standard deviation for this sample to be 7.1 (on a scale of 1 to 10) and 1.2, respectively. She used a 97% confidence level. However, she thinks that the confidence
You want to estimate the mean number of hours that students at your college work per week. Briefly explain how you will conduct this study using a small sample. Take a sample of 12 students from your college who hold a job. Collect data on the number of hours that these students spent working last
You want to estimate the proportion of people who are happy with their current jobs. Briefly explain how you will conduct this study. Take a sample of 35 persons and collect data on whether or not they are happy with their current jobs. Then estimate the population proportion. Choose your own
Multiple choice questions: 2. A 95% confidence interval for µ can be interpreted to mean that if we take 100 samples of the same size and construct 100 such confidence intervals for µ, then a. 95 of them will not include µ b. 95 will include µ c. 95 will include 3. The confidence level is
A sample of 36 vacation homes built during the past 2 years in a coastal resort region gave a mean construction cost of $159,000 with a population standard deviation of $27,000. a. What is the point estimate of the corresponding population mean? b. Make a 99% confidence interval for the mean
A sample of 25 malpractice lawsuits filed against doctors showed that the mean compensation awarded to the plaintiffs was $610,425 with a standard deviation of $94,820. Find a 95% confidence interval for the mean compensation awarded to plaintiffs of all such lawsuits. Assume that the compensations
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,
Briefly explain the meaning of each of the following terms. a. Null hypothesis b. Alternative hypothesis c. Critical point(s) d. Significance level e. Non-rejection region f. Rejection region g. Tails of a test h. Two types of errors
Write the null and alternative hypotheses for each of the following examples. Determine if each is a case of a two-tailed, a left-tailed, or a right-tailed test. a. To test if the mean amount of time spent per week watching sports on television by all adult men is different from 9.5 hours b. To
Consider the following null and alternative hypotheses: Ho: µ = 40 versus H1: µ ≠ 40 A random sample of 64 observations taken from this population produced a sample mean of 38.4. The population standard deviation is known to be 6. a. If this test is made at a 2% significance level, would you
Consider the following null and alternative hypotheses: Ho: p = .80 versus H1: p ≠ .82 A random sample of 600 observations taken from this population produced a sample proportion of .86. a. If this test is made at a 2% significance level, would you reject the null hypothesis? Use the
Consider the following null and alternative hypotheses: H0: p = .44 versus H1: p < .44 A random sample of 450 observations taken from this population produced a sample proportion of .39. a. If this test is made at a 2% significance level, would you reject the null hypothesis? Use the critical-value
According to the American Time Use Survey, Americans watched television each weekday for an average of 151 minutes in 2011 (Time, July 11, 2011). Suppose that this result is true for the 2011 population of all American adults. A recent sample of 120 American adults showed that they watch television
The mean consumption of water per household in a city was 1245 cubic feet per month. Due to a water shortage because of a drought, the city council campaigned for water use conservation by households. A few months after the campaign was started, the mean consumption of water for a sample of 100
A highway construction zone has a posted speed limit of 40 miles per hour. Workers working at the site claim that the mean speed of vehicles passing through this construction zone is at least 50 miles per hour. A random sample of 36 vehicles passing through this zone produced a mean speed of 48
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). A recent sample of 200 men from Ohio who got married for the first time this year showed that their average age at first marriage was 27.1 years. Assume that the
A real estate agent claims that the mean living area of all single-family homes in his county is at most 2400 square feet. A random sample of 50 such homes selected from this county produced the mean living area of 2540 square feet and a standard deviation of 472 square feet. a. Using α = .05, can
According to Moebs Services Inc., the cost of an individual checking account at U.S. community banks to these banks was between $175 and $200 in 2011 (Time, November 21, 2011). Suppose that the average annual cost of individual checking accounts at U.S. community banks to these banks was $190 in
Customers often complain about long waiting times at restaurants before the food is served. A restaurant claims that it serves food to its customers, on average, within 15 minutes after the order is placed. A local newspaper journalist wanted to check if the restaurant’s claim is true. A sample
What are the five steps of a test of hypothesis using the critical value approach? Explain briefly.
The customers at a bank complained about long lines and the time they had to spend waiting for service. It is known that the customers at this bank had to wait 8 minutes, on average, before being served. The management made some changes to reduce the waiting time for its customers. A sample of 60
The administrative office of a hospital claims that the mean waiting time for patients to get treatment in its emergency ward is 25 minutes. A random sample of 16 patients who received treatment in the emergency ward of this hospital produced a mean waiting time of 27.5 minutes with a standard
An earlier study claimed that U.S. adults spent an average of 114 minutes per day with their family. A recently taken sample of 25 adults from a city showed that they spend an average of 109 minutes per day with their family. The sample standard deviation is 11 minutes. Assume that the times spent
A computer company that recently introduced a new software product claims that the mean time taken to learn how to use this software is not more than 2 hours for people who are somewhat familiar with computers. A random sample of 12 such persons was selected. The following data give the times taken
A company claims that its 8-ounce low-fat yogurt cups contain, on average, at most 150 calories per cup. A consumer agency wanted to check whether or not this claim is true. A random sample of 10 such cups produced the following data on calories.Test using a 2.5% significance level whether the
According to the U.S. Census Bureau, 69% of children under the age of 18 years in the United States lived with two parents in 2009. Suppose that in a recent sample of 2000 children, 1298 were living with two parents. a. Using the critical value approach and α = .05, test whether the current
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,
More and more people are abandoning national brand products and buying store brand products to save money. The president of a company that produces national brand coffee claims that 40% of the people prefer to buy national brand coffee. A random sample of 700 people who buy coffee showed that 259
In a poll conducted by The New York Times and CBS News, 44% of Americans approve of the job that the Supreme Court is doing (The New York Times, June 8, 2012). Assume that this percentage was true for the population of Americans at the time of this poll was conducted. A recent poll of 1300
Mong Corporation makes auto batteries. The company claims that 80% of its LL70 batteries are good for 70 months or longer. A consumer agency wanted to check if this claim is true. The agency took a random sample of 40 such batteries and found that 75% of them were good for 70 months or longer. a.
Dartmouth Distribution Warehouse makes deliveries of a large number of products to its customers. To keep its customers happy and satisfied, the company’s policy is to deliver on time at least 90% of all the orders it receives from its customers. The quality control inspector at the company quite
Professor Hansen believes that some people have the ability to predict in advance the outcome of a spin of a roulette wheel. He takes 100 student volunteers to a casino. The roulette wheel has 38 numbers, each of which is equally likely to occur. Of these 38 numbers, 18 are red, 18 are black, and 2
Acme Bicycle Company makes derailleurs for mountain bikes. Usually no more than 4% of these parts are defective, but occasionally the machines that make them get out of adjustment and the rate of defectives exceeds 4%. To guard against this, the chief quality control inspector takes a random sample
Alpha Airline claims that only 15% of its flights arrive more than 10 minutes late. Let p be the proportion of all of Alpha’s flights that arrive more than 10 minutes late. Consider the hypothesis test H0: p < .15 versus H1: p > .15 Suppose we take a random sample of 50 flights by Alpha Airline
The standard therapy that is used to treat a disorder cures 60% of all patients in an average of 140 visits. A health care provider considers supporting a new therapy regime for the disorder if it is effective in reducing the number of visits while retaining the cure rate of the standard therapy. A
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 standard deviation of lives of these light bulbs is 400 hours. A skeptical consumer does not think that these light bulbs last as long as the
Thirty percent of all people who are inoculated with the current vaccine that is used to prevent a disease contract the disease within a year. The developer of a new vaccine that is intended to prevent this disease wishes to test for significant evidence that the new vaccine is more effective. a.
Since 1984, all automobiles have been manufactured with a middle tail-light. You have been hired to answer the following question: Is the middle tail-light effective in reducing the number of rear-end collisions? You have available to you any information you could possibly want about all rear-end
Before a championship football game, the referee is given a special commemorative coin to toss to decide which team will kick the ball first. Two minutes before game time, he receives an anonymous tip that the captain of one of the teams may have substituted a biased coin that has a 70% chance of
In Las Vegas, Nevada, and Atlantic City, New Jersey, tests are performed often on the various gaming devices used in casinos. For example, dice are often tested to determine if they are balanced. Suppose you are assigned the task of testing a die, using a two-tailed test to make sure that the
A statistician performs the test versus and finds the p-value to be .4546. a. The statistician performing the test does not tell you the value of the sample mean and the value of the test statistic. Despite this, you have enough information to determine the pair of p-values associated with the
You read an article that states “50 hypothesis tests of H0: µ = 35 versus H1: µ = 35 were performed using α = .05 on 50 different samples taken from the same population with a mean of 35. Of these, 47 tests failed to reject the null hypothesis.” Explain why this type of result is not
What is the difference between the critical value of z and the observed value of z?
Briefly explain the procedure used to calculate the p-value for a two-tailed and for a one-tailed test, respectively.
Find the p-value for each of the following hypothesis tests. a. Ho = µ = 23, H1 = µ ≠ 23, n = 50, = 21.25, σ = 5 b. Ho = µ = 15, H1 = µ < 15, n = 80, = 13.25, σ = 5.5 c. Ho = µ = 38, H1 = µ > 38, n = 35, = 40.25, σ = 7.2
Find the p-value for each of the following hypothesis tests. a. Ho = µ = 46, H1 = µ ≠ 46, n = 40, = 49.60, σ = 9.7 b. Ho = µ = 26, H1 = µ < 26, n = 33, = 24.30, σ = 4.3 c. Ho = µ = 18, H1 = µ > 18, n = 55, = 20.50, σ = 7.8
Consider Ho: µ = 29 versus H1: µ ≠ 29 A random sample of 25 observations taken from this population produced a sample mean of 25.3. The population is normally distributed with σ = 8. a. Calculate the p-value. b. Considering the p-value of part a, would you reject the null hypothesis if the
Consider Ho: µ = 72 versus H1: µ > 72. A random sample of 16 observations taken from this population produced a sample mean of 75.2. The population is normally distributed with σ = 6. a. Calculate the p-value. b. Considering the p-value of part a, would you reject the null hypothesis if the test
What are the four possible outcomes for a test of hypothesis? Show these outcomes by writing a table. Briefly describe the Type I and Type II errors.
For each of the following examples of tests of hypotheses about , show the rejection and non rejection regions on the sampling distribution of the sample mean assuming that it is normal. a. A two-tailed test with α = .05 and n = 40 b. A left-tailed test with α = .01 and n = 20 c. A right-tailed
For each of the following examples of tests of hypotheses about , show the rejection and non rejection regions on the sampling distribution of the sample mean assuming it is normal. a. A two-tailed test with α = .01 and n = 100 b. A left-tailed test with α = .005 and n = 27 c. A right-tailed
A random sample of 80 observations produced a sample mean of 86.50. Find the critical and observed values of z for each of the following tests of hypothesis using .10. The population standard deviation is known to be 7.20. a. H0: µ = 91 versus H1: µ ≠ 91 b. H0: µ = 91 versus H1: µ < 91
A random sample of 18 observations produced a sample mean of 9.24. Find the critical and observed values of z for each of the following tests of hypothesis using .05. The population standard deviation is known to be 5.40 and the population distribution is normal. a. H0: µ = 8.5 versus H1: µ
Consider the null hypothesis H0: µ = 625. Suppose that a random sample of 29 observations is taken from a normally distributed population with σ = 32. Using a significance level of .01, show the rejection and non-rejection regions on the sampling distribution curve of the sample mean and find the
Consider the null hypothesis H0: µ = 5. A random sample of 140 observations is taken from a population with σ = 17. Using α = .05, show the rejection and non-rejection regions on the sampling distribution curve of the sample mean and find the critical value(s) of z for the following. a. A
Explain how the tails of a test depend on the sign in the alternative hypothesis. Describe the signs in the null and alternative hypotheses for a two-tailed, a left-tailed, and a right-tailed test, respectively.
Consider H0: µ = 100 versus H1: µ ≠ 100. a. A random sample of 64 observations produced a sample mean of 98. Using α = .01, would you reject the null hypothesis? The population standard deviation is known to be 12. b. Another random sample of 64 observations taken from the same population
Consider H0: µ = 45 versus H1: µ < 45. a. A random sample of 25 observations produced a sample mean of 41.8. Using α = .025, would you reject the null hypothesis? The population is known to be normally distributed with σ = 6. b. Another random sample of 25 observations taken from the same
Make the following tests of hypotheses. a. H0: µ = 25, H1: µ ≠ 25, n = 81, = 28.5, σ = 3, α = .01 b. H0: µ = 12, H1: µ ≠ 12, n = 45, = 11.25, σ = 4.5, α = .05 c. H0: µ = 40, H1: µ ≠ 40, n = 100, = 47, σ = 7, α = .10
Make the following tests of hypotheses. a. H0: µ = 80, H1: µ ≠ 80, n = 81, = 76.5, σ = 15, α = .10 b. H0: µ = 32, H1: µ ≠ 32, n = 45, = 26.5, σ = 7.4, α = .01 c. H0: µ = 55, H1: µ ≠ 55, n = 100, = 60.5, σ = 4, α = .05
A consumer advocacy group suspects that a local supermarket’s 10-ounce packages of cheddar cheese actually weigh less than 10 ounces. The group took a random sample of 20 such packages and found that the mean weight for the sample was 9.955 ounces. The population follows a normal distribution
The manufacturer of a certain brand of auto batteries claims that the mean life of these batteries is 45 months. A consumer protection agency that wants to check this claim took a random sample of 24 such batteries and found that the mean life for this sample is 43.05 months. The lives of all such
A study claims that all adults spend an average of 14 hours or more on chores during a weekend. A researcher wanted to check if this claim is true. A random sample of 200 adults taken by this researcher showed that these adults spend an average of 14.65 hours on chores during a weekend. The
According to the U.S. Bureau of Labor Statistics, all workers in America who had a bachelor’s degree and were employed earned an average of $1038 a week in 2010. A recent sample of 400 American workers who have a bachelor’s degree showed that they earn an average of $1060 per week. Suppose that
According to the U.S. Postal Service, the average weight of mail received by Americans in 2011through the Postal Service was 57.2 pounds (The New York Times, December 4, 2011). One hundred randomly selected Americans were asked to keep all their mail for last year. It was found that they received
A telephone company claims that the mean duration of all long-distance phone calls made by its residential customers is 10 minutes. A random sample of 100 long-distance calls made by its residential customers taken from the records of this company showed that the mean duration of calls for this
Explain which of the following is a two-tailed test, a left-tailed test, or a right-tailed test. a. H0: µ = 45, H1: µ > 45 b. H0: µ = 23, H1: µ ≠ 23 c. H0: µ > 75, H1: µ < 75 Show the rejection and non-rejection regions for each of these cases by drawing a sampling distribution curve for
Lazurus Steel Corporation produces iron rods that are supposed to be 36 inches long. The machine that makes these rods does not produce each rod exactly 36 inches long. The lengths of the rods are normally distributed, and they vary slightly. It is known that when the machine is working properly,
At Farmer’s Dairy, a machine is set to fill 32-ounce milk cartons. However, this machine does not put exactly 32 ounces of milk into each carton; the amount varies slightly from carton to carton but has a normal distribution. It is known that when the machine is working properly, the mean net
According to Moebs Services Inc., an individual checking account at major U.S. banks costs these banks between $350 and $450 per year (Time, November 21, 2011). Suppose that the average cost of individual checking accounts at major U.S. banks was $400 for the year 2011. A bank consultant wants to
Records in a three-county area show that in the last few years, Girl Scouts sold an average of 47.93 boxes of cookies per year per girl scout, with a population standard deviation of 8.45 boxes per year. Fifty randomly selected Girl Scouts from the region sold an average of 46.54 boxes this year.
A journalist claims that all adults in her city spend an average of 30 hours or more per month on general reading, such as newspapers, magazines, novels, and so forth. A recent sample of 25 adults from this city showed that they spend an average of 27 hours per month on general reading. The
A study claims that all homeowners in a town spend an average of 8 hours or more on house cleaning and gardening during a weekend. A researcher wanted to check if this claim is true. A random sample of 20 homeowners taken by this researcher showed that they spend an average of 7.68 hours on such
A company claims that the mean net weight of the contents of its All Taste cereal boxes is at least 18 ounces. Suppose you want to test whether or not the claim of the company is true. Explain briefly how you would conduct this test using a large sample. Assume that α = .25 ounce.
Briefly explain the conditions that must hold true to use the t distribution to make a test of hypothesis about the population mean.
For each of the following examples of tests of hypothesis about , show the rejection and non rejection regions on the t distribution curve. a. A two-tailed test with α = .02 and n = 20 b. A left-tailed test with α = .01 and n = 16 c. A right-tailed test with α = .05 and n = 18
For each of the following examples of tests of hypothesis about , show the rejection and non rejection regions on the t distribution curve. a. A two-tailed test with α = .01 and n = 15 b. A left-tailed test with α = .005 and n = 25 c. A right-tailed test with α = .025 and n = 22
Explain which of the following is a two-tailed test, a left-tailed test, or a right-tailed test. a. H0: µ = 12, H1: µ < 12 b. H0: µ < 85, H1: µ > 85 c. H0: µ = 33, H1: µ ≠ 33 Show the rejection and non-rejection regions for each of these cases by drawing a sampling distribution curve for
A random sample of 14 observations taken from a population that is normally distributed produced a sample mean of 212.37 and a standard deviation of 16.35. Find the critical and observed values of t and the ranges for the p-value for each of the following tests of hypotheses, using α = .10. a. H0:
A random sample of 8 observations taken from a population that is normally distributed produced a sample mean of 44.98 and a standard deviation of 6.77. Find the critical and observed values of t and the ranges for the p-value for each of the following tests of hypotheses, using α = .05. a. H0: µ
Consider the null hypothesis H0: µ = 100. Suppose that a random sample of 35 observations is taken from this population to perform this test. Using a significance level of .01, show the rejection and non-rejection regions and find the critical value(s) of t when the alternative hypothesis is as

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