The mathematics department at a university wishes to administer a survey to a sample of students taking college algebra. The department is offering 32 sections of college algebra, similar in class size and makeup, with a total of 1280 students. They would like the sample size to be roughly 10% of the population of college algebra students this semester. How might the department obtain a simple random sample? A stratified sample? A cluster sample? Which method do you think is best in this situation?
> (a) Find the t-value such that the area in the right tail is 0.10 with 25 degrees of freedom. (b) Find the t-value such that the area in the right tail is 0.05 with 30 degrees of freedom. (c) Find the t-value such that the area left of the t-value is 0.
> The procedure for constructing a confidence interval about a mean is_____ , which means minor departures from normality do not affect the accuracy of the interval.
> True or False: To construct a confidence interval about the mean, the population from which the sample is drawn must be approximately normal.
> Put the following in order from narrowest to widest interval. Assume the sample size and sample proportion is the same for all four confidence intervals. (a) 95% confidence interval (b) 80% confidence interval (c) 99% confidence interval (d) 90% confiden
> If you constructed one hundred 95% confidence intervals based on one hundred different simple random samples of size n, how many of the intervals would you expect to include the unknown parameter? Assume all model requirements are satisfied.
> Target wants to open a new store in the village of Lockport. Before construction, Target’s marketers want to obtain some demographic information regarding the area under consideration. Design a sampling method to obtain the individuals in the sample. Be
> Define each of the following. (a) Point estimate (b) Confidence interval (c) Level of confidence (d) Margin of error
> The 116th House of Representatives of the United States of America has 435 members, of which 106 are women. An alien lands near the U.S. Capitol and treats members of the House as a random sample of the human race. He reports to his superiors that a 95%
> Two researchers, Jaime and Mariya, are each constructing confidence intervals for the proportion of a population who is left-handed. They find the point estimate is 0.13. Each independently constructed a confidence interval based on the point estimate, b
> Katrina wants to estimate the proportion of adult Americans who read at least 10 books last year. To do so, she obtains a simple random sample of 100 adult Americans and constructs a 95% confidence interval. Matthew also wants to estimate the proportion
> Why do polling companies often survey 1060 individuals when they wish to estimate a population proportion with a margin of error of 3% with 95% confidence?
> Explain why quadrupling the sample size causes the margin of error to be cut in half.
> What type of variable is required to construct a confidence interval for a population proportion?
> Explain what “95% confidence” means in a 95% confidence interval.
> The American Society for Microbiology (ASM) and the Soap and Detergent Association (SDA) jointly commissioned two separate studies, both of which were conducted by Harris Interactive. In one of the studies, 1001 adults were interviewed by telephone an
> Alan wants to estimate the proportion of adults who walk to work. In a survey of 10 adults, he finds 1 who walks to work. Explain why a 95% confidence interval using the normal model yields silly results. Then compute and interpret a 95% confidence inter
> A school board at a local community college is considering raising the student services fees. The board wants to obtain the opinion of the student body before proceeding. Design a sampling method to obtain the individuals in the sample. Be sure to suppor
> Jane wants to estimate the proportion of students on her campus who eat cauliflower. After surveying 20 students, she finds 2 who eat cauliflower. Obtain and interpret a 95% confidence interval for the proportion of students who eat cauliflower on Jane’s
> A Bernoulli random variable is a variable that is either 0 (a failure) or 1 (a success). The probability of success is denoted p. (a) Use a statistical spreadsheet to generate 1000 Bernoulli samples of size n = 20 with p = 0.15. (b) Determine the sample
> CNN polled 702 likely voters immediately preceding the 2018 Arizona senate race. The results of the survey indicated that Kyrsten Sinema had the support of 51% of respondents, while Martha McSally had support of 47%. The poll’s margin of error was 4.4%.
> In a Gallup Poll, 44% of the people polled answered “more strict” to the following question: “Do you feel that the laws covering the sale of firearms should be made more strict, less strict, or kept as they are now?” Suppose the margin of error in the po
> In a Gallup poll, 64% of the people polled answered yes to the following question: “Are you in favor of the death penalty for a person convicted of murder?” The margin of error in the poll was 3%, and the estimate was made with 95% confidence. At least h
> A sociologist wishes to conduct a poll to estimate the percentage of Americans who favor affirmative action programs for women and minorities for admission to colleges and universities. What sample size should be obtained if she wishes the estimate to be
> A television sports commentator wants to estimate the proportion of Americans who follow professional football. What sample size should be obtained if he wants to be within 3 percentage points with 95% confidence if (a) he uses a 2010 estimate of 53% ob
> A school administrator is concerned about the amount of credit-card debt that college students have. She wishes to conduct a poll to estimate the percentage of full-time college students who have credit-card debt of $2000 or more. What size sample should
> A researcher for the U.S. Department of the Treasury wishes to estimate the percentage of Americans who support abolishing the penny. What size sample should be obtained if he wishes the estimate to be within 2 percentage points with 98% confidence if (a
> An urban economist wishes to estimate the proportion of Americans who own their homes. What size sample should be obtained if he wishes the estimate to be within 0.02 with 90% confidence if (a) he uses a 2010 estimate of 0.669 obtained from the U.S. Cens
> The city of Naperville is considering the construction of a new commuter rail station. The city wishes to survey the residents of the city to obtain their opinion regarding the use of tax dollars for this purpose. Design a sampling method to obtain the i
> A researcher wishes to estimate the proportion of households that have broadband Internet access. What size sample should be obtained if she wishes the estimate to be within 0.03 with 99% confidence if (a) she uses a 2009 estimate of 0.635 obtained from
> Go to www.pearsonhighered.com/ sullivanstats to obtain the data file 9_1_34 using the file format of your choice for the version of the text you are using. The data represent the daily (for example, Monday to Tuesday) movement of Johnson & Johnson (JNJ)
> The data set “Tornadoes_2017” located at www.pearsonhighered.com/ sullivanstats contains a variety of variables that were measured for all tornadoes in the United States in 2017. (a) The F scale is used to describe the range of wind speeds of a tornado.
> The Sullivan Statistics Survey I asks, “Would you be willing to pay higher taxes if the tax revenue went directly toward deficit reduction?” Treat the survey respondents as a random sample of adult Americans. Go to www.pearsonhighered.com/sullivanstats t
> In a survey conducted by the marketing agency 11mark, 241 of 1000 adults 19 years of age or older confessed to bringing and using their cell phone every trip to the bathroom (confessions included texting and answering phone calls). (a) What is the sample
> In a survey of 700 community college students, 481 indicated that they have read a book for personal enjoyment during the school year (based on data from the Community College Survey of Student Engagement). (a) Determine a 90% confidence interval for the
> Low levels of testosterone in adult males may be treated using AndroGel 1.62%. In clinical studies of 234 adult males who were being treated with AndroGel 1.62%, it was found that 26 saw their prostate-specific antigen (PSA) elevated. The PSA is a protei
> In a USA Today/Gallup poll, 768 of 1024 randomly selected adult Americans aged 18 or older stated that a candidate’s positions on the issue of family values are extremely or very important in determining their vote for president. (a) Obtain a point estim
> A random sample of 1003 adult Americans was asked, “Do you pretty much think televisions are a necessity or a luxury you could do without?” Of the 1003 adults surveyed, 521 indicated that televisions are a luxury they could do without. (a) Obtain a point
> Relative to other nations, how do fourth-graders in the United States rank in terms of reading and math ability? Are they in the bottom 50% or in the top 50%? In a survey of 700 randomly sampled registered voters in the United States conducted by Conques
> To obtain students’ opinions about proposed changes to course registration procedures, the administration of a small college asked for faculty volunteers who were willing to administer a survey in one of their classes. Twenty-three faculty members volunt
> A survey of 2306 adult Americans aged 18 and older conducted by Harris Interactive found that 417 have donated blood in the past two years. (a) Obtain a point estimate for the population proportion of adult Americans aged 18 and older who have donated bl
> A Gallup poll of 547 adult Americans employed full or part time asked, “Generally speaking, would you say your commute to work is— very stressful, somewhat stressful, not that stressful, or not stressful at all?” Gallup reported that 24% of American work
> A Rasmussen Reports national survey of l000 adult Americans found that 18% dreaded Valentine’s Day. The margin of error for the survey was 4.5 percentage points with 95% confidence. Explain what this means.
> A USA Today/Gallup poll asked l006 adult Americans how much it would bother them to stay in a room on the 13th floor of a hotel. Interestingly, 13% said it would bother them. The margin of error was 3 percentage points with 95% confidence. Which of the f
> In response to the Great Depression, Franklin D. Roosevelt enacted many New Deal policies. One such policy was the enactment of the National Recovery Administration (NRA), which required businesses to agree to wages and prices within their particular ind
> x = 540, n = 900, 96% confidence
> x = 860, n = 1100, 94% confidence
> x = 400, n = 1200, 95% confidence
> x = 120, n = 500, 99% confidence
> x = 80, n = 200, 98% confidence
> x = 30, n = 150, 90% confidence
> Lower bound: 0.853, upper bound: 0.871, n = 10,732
> Lower bound: 0.462, upper bound: 0.509, n = 1680
> Lower bound: 0.051, upper bound: 0.074, n = 1120
> Lower bound: 0.201, upper bound: 0.249, n = 1200
> 92%
> 98%
> 99%
> 90%
> As the level of confidence of a confidence interval increases, the margin of error_____ (increases/decreases). As the sample size used to obtain a confidence interval increases, the margin of error______ (increases/decreases).
> To predict the outcome of a county election, a newspaper obtains a list of all 945,035 registered voters in the county and wants to conduct a systematic sample. (a) Determine k if the sample size is 130. (b) Determine the individuals who will be administ
> True or False: A 95% confidence interval for a population proportion with lower bound 0.45 and upper bound 0.51 means there is a 95% probability the population proportion is between 0.45 and 0.51
> If a sample proportion is 0.55, which of the following could be a 90% confidence interval for the population proportion? Select all that apply. (a) Lower bound: 0.50; Upper bound: 0.60 (b) Lower bound: 0.53; Upper bound: 0.59 (c) Lower bound: 0.52; Upper
> The ___ ____, denoted /, is given by the formula / = _____ , where x is the number of individuals with a specified characteristic in a sample of n individuals.
> In a town of 500 households, 220 have a dog. The population proportion of dog owners in this town (expressed as a decimal) is p =______ .
> The New England Patriots made headlines prior to the 2015 Super Bowl for allegedly playing with underinflated footballs. An underinflated ball is easier to grip, and therefore, less likely to be fumbled. What do the data say? The following data represent
> In this section, we assumed that the sample size was less than 5% of the size of the population. When sampling without replacement from a finite population in which n > 0.05N, the standard deviation of the distribution of / is given by where N is the si
> In Chapter 6, we learned that the proportion of passengers who miss a flight for which they have a reservation is 0.0995. (a) Suppose a flight has 290 reservations. What is the probability that 25 or more passengers will miss the flight? (b) Suppose a fl
> Consider the homeowners association presented at the beginning of this section. A random sample of 20 households resulted in 15 indicating that they would favor an increase in assessments. Explain why the normal model could not be used to determine if a
> Suppose 21% of all American teens (age 13–17 years) believe in reincarnation. (a) Bob and Alicia both obtain a random sample of 100 American teens and ask each participant to disclose whether they believe in reincarnation or not. Is “belief in reincarnat
> A researcher studying ADHD among teenagers obtains a simple random sample of 100 teenagers aged 13–17 and asks them whether or not they have ever been prescribed medication for ADHD. To say that the distribution of /, the sample proportion of teenagers w
> The human resource department at a certain company wants to conduct a survey regarding worker morale. The department has an alphabetical list of all 4502 employees at the company and wants to conduct a systematic sample. (a) Determine k if the sample siz
> A researcher studying public opinion of proposed Social Security changes obtains a simple random sample of 50 adult Americans and asks them whether or not they support the proposed changes. To say that the distribution of /, the sample proportion of adul
> A shipment of 50,000 transistors arrives at a manufacturing plant. The quality control engineer at the plant obtains a random sample of 500 resistors and will reject the entire shipment if 10 or more of the resistors are defective. Suppose that 4% of the
> Exit polling is a popular technique used to determine the outcome of an election prior to results being tallied. Suppose a referendum to increase funding for education is on the ballot in a large town (voting population over 100,000). An exit poll of 310
> The Pew Research Center recently reported that 18% of women 40–44 years of age have never given birth. Suppose a random sample of 250 adult women 40–44 years of age results in 52 indicating they have never given birth. Explain why this is not necessarily
> According to a study conducted by the Gallup organization, the proportion of Americans who are afraid to fly is 0.10. A random sample of 1100 Americans results in 121 indicating that they are afraid to fly. Explain why this is not necessarily evidence th
> According to creditcard.com, 29% of adults do not own a credit card. (a) Suppose a random sample of 500 adults is asked, “Do you own a credit card?” Describe the sampling distribution of /, the proportion of adults who do not own a credit card. (b) What
> According to a study done by the Pew Research Center, 39% of adult Americans believe that marriage is now obsolete. (a) Suppose a random sample of 500 adult Americans is asked whether marriage is obsolete. Describe the sampling distribution of /, the pro
> According to a study done by the Gallup organization, the proportion of Americans who are satisfied with the way things are going in their lives is 0.82. (a) Suppose a random sample of 100 Americans is asked, “Are you satisfied with the way things are go
> According to a study done by Wakefield Research, the proportion of Americans who can order a meal in a foreign language is 0.47. (a) Suppose a random sample of 200 Americans is asked to disclose whether they can order a meal in a foreign language. Is the
> A simple random sample of size n = 1460 is obtained from a population whose size is N = 1,500,000 and whose population proportion with a specified characteristic is p = 0.42. (a) Describe the sampling distribution of /. (b) What is the probability of obt
> The owner of a private food store is concerned about employee morale. She decides to survey the managers and hourly employees to see if she can learn about work environment and job satisfaction. From the list of workers at the store, obtain a stratified
> A simple random sample of size n = 1000 is obtained from a population whose size is N = 1,000,000 and whose population proportion with a specified characteristic is p = 0.35. (a) Describe the sampling distribution of /. (b) What is the probability of o
> A simple random sample of size n = 200 is obtained from a population whose size is N = 25,000 and whose population proportion with a specified characteristic is p = 0.65. (a) Describe the sampling distribution of /. (b) What is the probability of obtaini
> A simple random sample of size n = 75 is obtained from a population whose size is N = 10,000 and whose population proportion with a specified characteristic is p = 0.8. (a) Describe the sampling distribution of /. (b) What is the probability of obtaining
> n = 1010, p = 0.84
> n = 1000, p = 0.103
> n = 300, p = 0.7
> n = 500, p = 0.4
> What happens to the standard deviation of / as the sample size increases? If the sample size is increased by a factor of 4, what happens to the standard deviation of /?
> Describe the circumstances under which the shape of the sampling distribution of / is approximately normal.
> True or False: The mean of the sampling distribution of / is p.
> The Future Government Club wants to sponsor a panel discussion on the upcoming national election. The club wants to have four of its members lead the panel discussion. To be fair, however, the panel should consist of two Democrats and two Republicans. Fr
> True or False: The population proportion and sample proportion always have the same value.
> True or False: The distribution of the sample mean, /, will be approximately normally distributed if the sample is obtained from a population that is normally distributed, regardless of the sample size.
> The standard deviation of the sampling distribution of / is called the ____ ____of the____.
> Suppose a simple random sample of size is drawn from a large population with mean and standard deviation . The sampling distribution of / and standard deviation /
> The of the sample mean, /, is the probability distribution of all possible values of the random variable / computed from a sample of size n from a population with mean and standard deviation
> A bull market is defined as a market condition in which the price of a security rises for an extended period of time. A bull market in the stock market is often defined as a condition in which a market rises by 20% or more without a 20% decline. The data
> Suppose you want to study the number of hours of sleep full-time college students at your college get each evening. To do so, you obtain a list of full-time students at your college, obtain a simple random sample of ten students, and ask each of them to
