Question: List the eight properties of the linear

> Determine whether the random variable is discrete or continuous. In each case, state the possible values of the random variable. (a) The number of students in a randomly selected elementary school classroom (b) The amount of snow that falls in Minneapoli

> Suppose that P(E) = 0.8, P(F) = 0.5, and P(E and F) = 0.24. Are events E and F independent? Why?

> Suppose that events E and F are independent. In addition, P(E) = 0.45 and P(F) = 0.2. What is P(E and F)?

> Generally, the goal of an experiment is to determine the effect that treatments will have on the response variable.

> Suppose that P(E) = 0.36, P(F) = 0.12, and E and F are mutually exclusive. What is P(E or F)?

> Suppose that P(E) = 0.76, P(F) = 0.45, and P(E and F) = 0.32. What is P(E or F)?

> Suppose that E = {yellow}. Compute the probability of Ec.

> E = {red or blue or yellow}

> (a) Patti and John each played 100 games of Solitaire on their smart phone. Patti won 7 of her games and estimated the probability of winning Solitaire as 0.07. John won 6 of his games and estimated the probability of winning Solitaire as 0.06. Why are t

> The following data represent the number of cases of coffee or filters sold by four sales reps in a recent sales competition. (a) What is the probability that a randomly selected case was sold by Bryce? Is this unusual? (b) What is the probability that a

> In 1996, a New York couple won $2.5 million in the state lottery. Eleven years later, the couple won $5 million in the state lottery using the same set of numbers. The odds of winning the New York lottery twice are roughly 1 in 16 trillion, described by

> During the 1998 Major League Baseball season, Mark McGwire of the St. Louis Cardinals hit 70 home runs. Of the 70 home runs, 34 went to left field, 20 went to left center field, 13 went to center field, 3 went to right center field, and 0 went to right f

> F = {green or orange}

> In the game of five-card stud, one card is dealt face down to each player and the remaining four cards are dealt face up. After two cards are dealt (one down and one up), the players bet. Players continue to bet after each additional card is dealt. Suppo

> Distinguish between nonsampling error and sampling error.

> Explain what is meant by a subjective probability. List some examples of subjective probabilities.

> Use a graphing calculator or statistical software to simulate the playing of the game of roulette, using an integer distribution with numbers 1 through 38. Repeat the simulation 100 times. Let the number 37 represent 0 and the number 38 represent 00. Use

> Because of a mistake in packaging, a case of 12 bottles of red wine contained five Merlot and seven Cabernet, each without labels. All the bottles look alike and have an equal probability of being chosen. Three bottles are randomly selected. (a) What is

> In one of Arizona’s lotteries, balls are numbered 1–35. Five balls are selected randomly, without replacement. The order in which the balls are selected does not matter. To win, your numbers must match the five selected. Determine your probability of win

> How many different simple random samples of size 8 can be obtained from a population whose size is 55?

> How many different vertical arrangements are there of 10 flags if 4 are white, 3 are blue, 2 are green, and 1 is red?

> If four students enter a classroom that has 10 vacant seats, in how many ways can they be seated?

> A license plate is designed so that the first two characters are letters and the last four characters are digits (0 through 9). How many different license plates can be formed assuming that letters and numbers can be used more than once?

> Suppose that you draw 3 cards without replacement from a standard 52-card deck. What is the probability that all 3 cards are aces?

> E = {yellow}

> Match each word or phrase to the definition.

> The Illinois Lottery’s PICK 4 game is similar to PICK 3, except a player must match a sequence of four repeatable numbers, ranging from 0 to 9, in exact order (for example, 5–8–5–1). With a single ticket, what is the probability of matching the four winn

> For the Illinois Lottery’s PICK 3 game, a player must match a sequence of three repeatable numbers, ranging from 0 to 9, in exact order (for example, 3–7–2). With a single ticket, what is the probability of matching the three winning numbers?

> According to the National Constitution Center, 18% of Americans trust organized religion. (a) If an American is randomly selected, what is the probability he or she trusts organized religion? (b) If an American is randomly selected, what is the probabili

> The following data represent the birth weights (in grams) of babies born in 2017, along with the period of gestation. (a) What is the probability that a randomly selected baby born in 2017 was postterm? (b) What is the probability that a randomly selecte

> In a poll conducted by Genworth Financial, a random sample of adults was asked, “What age would you like to live to?” The results of the survey are given in the table. (a)Construct a probability model of the data. (b) Is it unusual for an individual to w

> In 2016, there were 34,439 traffic fatalities in the United States. Of these, 9477 were alcohol related. (a) What is the probability that a randomly selected traffic fatality in 2016 was alcohol related? (b) What is the probability that a randomly select

> In the game of roulette, a wheel consists of 38 slots, numbered 0, 00, 1, 2,…., 36. (See the photo in Problem 27 from Section 5.1.) To play the game, a metal ball is spun around the wheel and allowed to fall into one of the numbered slots. The slots numb

> Determine the value of each of the following: (a) 7! (b) 0! (c) 9C4 (d) 10C3 (e) 9P2 (f) 12P4

> Suppose that P(E and F) = 0.35 and P(F) = 0.7. What is P(E | F)?

> Suppose that P(E) = 0.59 and P(F | E) = 0.45. What is P(E and F)?

> What does it mean when a part of the population is under- represented?

> (a) Which among the following numbers could be the probability of an event? 0, -0.01, 0.75, 0.41, 1.34 (b) Which among the following numbers could be the probability of an event?

> The correlation between the number of visitors to the state of Florida and the number of shark attacks since 1990 is 0.946. Should the number of visitors to Florida be reduced in an attempt to reduce shark attacks? Explain your reasoning. Source: Florida

> Use Queens data and the results from Problems 3 and 5 to compute and interpret R2.

> Use the results from Problems 2 and 4 to compute and interpret R2.

> (a) Draw a scatter diagram treating x as the explanatory variable and y as the response variable. (b) Select two points from the scatter diagram, and find the equation of the line containing the points selected. (c) Graph the line found in part (b) on th

> Using the Queens data and results from Problem 3, do the following: (a) Find the least-squares regression line, treating square footage as the explanatory variable. (b) Interpret the slope and y-intercept, if appropriate. (c) Is the rent on the 825-squar

> Using the data and results from Problem 2, do the following: (a) Find the least-squares regression line treating fat content as the explanatory variable. (b) Draw the least-squares regression line on the scatter diagram. (c) Interpret the slope and y-int

> The following data represent the square footage and rent for apartments in the borough of Queens and Nassau County, New York. (a) On the same graph, draw a scatter diagram for both Queens and Nassau County apartments treating square footage as the explan

> A nutritionist was interested in developing a model that describes the relation between the amount of fat (in grams) in cheeseburgers at fast-food restaurants and the number of calories. She obtains the following data from the websites of the companies.

> In studies of monozygotic (identical) twins, the correlation of intelligence (IQ) scores is 0.85. (a) What or who are the individuals in this scenario? (b) What are the variables? (c) What proportion of the variability in one twin’s IQ is explained by th

> What is a closed question? What is an open question? Discuss the advantages and disadvantages of each type of question.

> In a newspaper article written in the Chicago Tribune, it was claimed that poorer school districts have shorter school days. (a) The following scatter diagram was drawn using the data supplied in the article. In this scatter diagram, the response variabl

> (a) The correlation between number of married residents and number of unemployed residents for the 50 states and Washington, DC, is 0.922. A scatter diagram of the data is shown. What type of relation appears to exist between number of marriages and numb

> Recessions are defined as two consecutive quarters of reduced national output. One measure to assess the severity of a recession is the rate of unemployment. The table shows the number of employed and unemployed residents of the United States at the peak

> Are you more likely to be satisfied with your automobile purchase when it is new or used? The following data represent the level of satisfaction of the buyer for both new and used cars. (a) How many were extremely satisfied with their automobile purchase

> In sports betting, Las Vegas sports books establish winning margins for a team that is favored to win a game. An individual can place a wager on the game and will win if the team bet upon wins after accounting for the spread. For example, if Team A is fa

> On October 6, 2010, Roy Halladay of the Philadelphia Phillies threw the second post-season no-hitter in Major League history. The side-by-side boxplot shows the pitch speed (in miles per hour) for all of Halladay’s pitches during the game. (a) Which pitc

> According to the National Center for Health Statistics, the mean weight of a 20- to 29-year-old female is 156.5 pounds, with a standard deviation of 51.2 pounds. The mean weight of a 20- to 29-year-old male is 183.4 pounds, with a standard deviation of 4

> Michael has just completed his first semester in college. He earned an A in his five-hour calculus course, a B in his four-hour chemistry course, an A in his three-hour speech course, and a C in his three-hour psychology course. Assuming an A equals 4 po

> The frequency distribution listed in the table represents the travel time to work (in minutes) for a random sample of 895 U.S. adults. (a) Approximate the mean travel time to work for U.S. adults. (b) Approximate the standard deviation travel time to wor

> Discuss a possible advantage of offering rewards or incentives to increase response rates. Are there any disadvantages?

> Volume of water lost each day through a leaky faucet

> Suppose that a certain brand of light bulb has a mean life of 600 hours and a standard deviation of 53 hours. (a) A histogram of the data indicates the sample data follow a bell-shaped distribution. According to the Empirical Rule, 99.7% of light bulbs h

> As part of a statistics project, a student surveys 30 randomly selected students and asks them how many speeding tickets they have been issued in the past month. The results of the survey are as follows: (a) Draw a frequency histogram of the data and des

> The following data represent the ages of chief justices of the U.S. Supreme Court when they were appointed. (a) Determine the population mean, median, and mode ages. (b) Determine the range and population standard deviation ages. (c) Obtain two simple ra

> The following data represent the sales price (in dollars) for nine 2-year-old Chevrolet Cobalts in the Los Angeles area. (a) Determine the sample mean and median price. (b) Determine the range, sample standard deviation, and interquartile range. (c) Redo

> One method of estimating body fat is through skinfold thickness measurement using from three to nine different standard anatomical sites around the body from the right side only (for consistency). The tester pinches the skin at the appropriate site to ra

> According to the National Center for Health Statistics, a 19-year-old female whose height is 67.1 inches has a height that is at the 85th percentile. Explain what this means.

> Ever wonder how many words are in a typical inaugural address? The data in the next column represent the lengths of all the inaugural addresses (measured in word count) for all presidents up to Donald Trump. (a) Determine the mean and median number of wo

> The following data represent the muzzle velocity (in meters per second) of rounds fired from a 155-mm gun. Source: Christenson, Ronald, and Blackwood, Larry, “Tests for Precision and Accuracy of Multiple Measuring Devices,” Technometrics, 35(4): 411–421,

> Inflation The side-by-side bar graph to the right shows the average grade point average for the academic years beginning in 1983, 1988, 1993, 1998, 2003, 2008, and 2013, for colleges and universities. (a) Does the graph suggest that grade inflation is a

> The data on the following page represent the average number of hours per week that a random sample of 40 college students spend online. The data are based on the ECAR Study of Undergraduate Students and Information Technology. Construct a stem-and-leaf d

> Suppose a survey asks, “How many hours do you study?” Explain how this could be interpreted in more than one way. Suggest a way in which the question could be improved.

> The following data represent the diameter (in inches) of a random sample of 34 Keebler Chips Deluxe™ Chocolate Chip Cookies. (a) Construct a frequency distribution. (b) Construct a relative frequency distribution. (c) Construct a frequency histogram. Des

> The table shows the home ownership rate in each of the 50 states and Washington, DC, in 2017. Note: The state with the highest home ownership rate is West Virginia and the lowest is Washington, DC. With a lower class limit of the first class of 45 and a

> A random sample of 60 couples married for seven years were asked to give the number of children they have. The results of the survey are as follows: (a) Construct a frequency distribution of the data. (b) Construct a relative frequency distribution of th

> One hundred randomly selected registered voters in the city of Naperville were asked their political affiliation: Democrat (D), Republican (R), or Independent (I). The results of the survey are shown below. (a) Construct a frequency distribution of the d

> The frequency distribution on the following page represents the number of live births (in thousands) in the United States in 2016 by age of mother. (a) Construct a relative frequency distribution. (b) Construct a frequency histogram. Describe the shape o

> The following frequency distribution represents the cause of death in homicides for a random sample of homicides. (a) Construct a relative frequency distribution. (b) Construct a relative frequency bar graph. (c) Construct a pie chart.

> The graphic to the right is a USA Today—type graph displaying women’s preference for shoes. (a) Which type of shoe is preferred the most? The least? (b) How is the graph misleading?

> In 2017, the average earnings of a high school graduate were $30,624. At $52,484, the average earnings of a recipient of a bachelor’s degree were about 71% higher. Source: U.S. Census Bureau. (a) Construct a misleading graph that a college recruiter migh

> The following data represent the percentage of total adjusted gross income (AGI) earned and percentage of tax paid by various income classes. The top 1% represents the percentage of total AGI earned and tax paid by those whose income is higher than 99% o

> Harris Interactive conducted a poll of U.S. adults and asked, “When there is a voiceover in a commercial, which type of voice is more likely to sell me a car?” Results of the survey are in the bar graph. (a) How many participants were in the survey? (b)

> Discuss why the order of questions or choices within a questionnaire are important in sample surveys.

> What is the role of randomization in a designed experiment? If you were conducting a completely randomized design with four treatments and 100 experimental units, describe how you would randomly assign the experimental units to the treatments.

> Many newspaper articles discuss the dangers of teens texting while driving. Suppose you are a journalist and want to chime in on the discussion. However, you want your article to be more compelling, so you decide to conduct an experiment with one hundred

> Go to an online science magazine such as Science Daily (www.sciencedaily.com) or an open source online medical journal such as BioMed Central (www.biomedcentral.com) and identify an article that includes statistical research. (a) Was the study you select

> Describe what is meant by a matched-pairs design. Contrast this experimental design with a completely randomized design.

> A marketing research firm wants to know whether information presented in a commercial is better recalled when presented using humor or serious commentary by adults between 18 and 35 years of age. They will use an exam that asks questions of 50 subjects a

> A common tip for taking multiple-choice tests is to always pick (b) or (c) if you are unsure. The idea is that instructors tend to feel the answer is more hidden if it is surrounded by distractor answers. An astute statistics instructor is aware of this

> Researchers wanted to assess the effect of low alcohol consumption on reaction time in seniors, believing that even low levels of alcohol consumption can impair the ability to walk, thereby increasing the likelihood of falling. They identified 13 healthy

> Smoking and drinking coffee have a tendency to stain teeth. In an effort to determine the ability of chewing gum to remove stains on teeth, researchers conducted an experiment in which 64 bovine incisors (teeth) were stained with natural pigments such as

> Based on the Military Standard 105E (ANS1/ASQC Z1.4, ISO 2859) Tables, a lot of 91 to 150 items with an acceptable quality level (AQL) of 1% and a normal inspection plan would require a sample of size 13 to be inspected for defects. If the sample contain

> A quality-control engineer wants to be sure that bolts coming off an assembly line are within prescribed tolerances. He wants to conduct a systematic sample by selecting every 9th bolt to come off the assembly line. The machine produces 30,000 bolts per

> Why is a high response rate desired? How would a low response rate affect survey results?

> The mayor of a town wants to conduct personal interviews with small business owners to determine if there is anything he could do to help improve business conditions. The following list gives the names of the companies in the town. Obtain a simple random

> Each of the following surveys has bias. Determine the type of bias and suggest a remedy. (a) A politician sends a survey about tax issues to a random sample of subscribers to a literary magazine. (b) An interviewer with little foreign language knowledge

> Officers for the Department of Motor Vehicles pull aside every 40th tractor trailer passing through a weigh station, starting with the 12th, for an emissions test.

> Thirty-five sophomores, 22 juniors, and 35 seniors are randomly selected to participate in a study from 574 sophomores, 462 juniors, and 532 seniors at a certain high school.

> An Internet service provider randomly selects 15 residential blocks from a large city and surveys every household in these 15 blocks to determine the number that would use a high-speed Internet service.

> On election day, a pollster for Fox News positions herself outside a polling place near her home and asks the first 50 voters leaving the facility to complete a survey.

> Read the following description of an observational study and determine whether it is a cross-sectional, a case-control, or a cohort study. Explain your choice. The Cancer Prevention Study II (CPS-II) examines the relationship among environmental and life

> A sample of 504 patients in early stages of Alzheimer’s disease is divided into two groups. One group receives an experimental drug; the other receives a placebo. The advance of the disease in the patients from the two groups is tracked at 1-month interv