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statistics
Questions and Answers of
Statistics
The linear correlation between violent crime rate and percentage of the population that has a cell phone is -0.918 for years since 1995. Do you believe that increasing the percentage of the
Consider the following set of data:(a) Draw a scatter diagram of the data and compute the linear correlation coefï¬cient.(b) Draw a scatter diagram of the data and compute the linear correlation
Consider the following data set:(a) Draw a scatter diagram with the x-axis starting at 0 and ending at 30 and with the y-axis starting at 0 and ending at 20.(b) Compute the linear correlation
Theodore Coladarci and Irv Kornfield from the University of Maine found a correlation of 0.68 between responses to questions on the RateMyProfessors.com Web site and typical in-class evaluations.
Explain what is wrong with the following statement: “We have concluded that a high correlation exists between the gender of drivers and rates of automobile accidents.” Suggest a better way to
Draw a scatter diagram that might represent the relation between the number of minutes spent exercising on an elliptical and calories burned. Draw a scatter diagram that might represent the relation
Suppose you work a part-time job and earn $15 per hour. Draw a scatter diagram that might represent the relation between your gross pay and hours worked. Is this a deterministic relation or a
For the data set(a) Draw a scatter diagram. Comment on the type of relation that appears to exist between x and y.(b) Given that x̄ = 3.6667, sx = 2.4221, y-bar = 3.9333, sy = 1.8239, and r =
For the data set(a) Draw a scatter diagram. Comment on the type of relation that appears to exist between x and y.(b) Given that x̄ = 6.2, sx = 3.03315, y-bar = 2.04, sy = 0.461519, and r =
(a) By hand, 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 ï¬nd the equation of the line
(a) By hand, 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 ï¬nd the equation of the line
(a) By hand, 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 ï¬nd the equation of the line
(a) By hand, 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 ï¬nd the equation of the line
(a) By hand, 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 ï¬nd the equation of the line
(a) By hand, 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 ï¬nd the equation of the line
A student at Joliet Junior College conducted a survey of 20 randomly selected full-time students to determine the relation between the number of hours of video game playing each week, x, and
After the first exam in a statistics course, Professor Katula surveyed 14 randomly selected students to determine the relation between the amount of time they spent studying for the exam and exam
In his best-selling book Moneyball, author Michael Lewis discusses how statistics can be used to judge both a baseball player’s potential and a team’s ability to win games. One aspect of this
The least-squares regression equation y-hat = 0.7676x - 52.6841 relates the carbon dioxide emissions (in hundred thousands of tons), y, and energy produced (hundred thousands of megawatts), x, for
The following data represent commute times (in minutes) and score on a well-being survey. Commute Time Gallup-Healthways Well-Being (minutes), x ....... Index Composite Score, y 5 .......... 69.2 15
An economist wants to determine the relation between one’s FICO score, x, and the interest rate of a 36-month auto loan, y. The given data represent the interest rate (in percent) a bank would
A pediatrician wants to determine the relation that exists between a childs height, x, and head circumference, y. She randomly selects 11 children from her practice, measures their
The American black bear (Ursus americanus) is one of eight bear species in the world. It is the smallest North American bear and the most common bear species on the planet. In 1969, Dr. Michael R.
An engineer wants to determine how the weight of a car, x, affects gas mileage, y. The following data represent the weights of various domestic cars and their miles per gallon in the city for the
Research performed at NASA and led by Emily R. Morey-Holton measured the lengths of the right humerus and right tibia in 11 rats who were sent to space on Spacelab Life Sciences 2. The following data
Example 5 in Section 4.1 on page 185 discussed the effect of cola consumption on bone mineral density in the femoral neck of women. (a) Find the least-squares regression line treating cola
The following data represent the number of days absent, x, and the ï¬nal grade, y, for a sample of college students in a general education course at a large state university.(a) Find
The following data represent the total compensation for 10 randomly selected chief executive ofï¬cers (CEO) and the company’s stock performance in 2009. Based on the analysis from Problem
Researchers wondered whether the size of a person’s brain was related to the individual’s mental capacity. They selected a sample of right-handed introductory psychology students who had SAT
The following data represent the number of licensed drivers in various age groups and the number of fatal accidents within the age group by gender.(a) Find the least-squares regression line for males
One of the biggest factors in determining the value of a home is the square footage. The following data represent the square footage and asking price (in thousands of dollars) for a random sample of
It is well known that women should not smoke while pregnant, but what is the effect of smoking on a babys birth weight? Researchers Ira M. Bernstein and associates sought to
Explain the phrase outside the scope of the model. Why is it dangerous to make predictions outside the scope of the model?
Match the coefï¬cient of determination to the scatter diagram. The scales on the horizontal and vertical axis are the same for each scatter diagram.(a) R2 = 0.58(b) R2 = 0.90(c) R2 =
Use the linear correlation coefficient given to determine the coefficient of determination, R2. Interpret each R2.(a) r = -0.32(b) r = 0.13(c) r = 0.40(d) r = 0.93
An Unhealthy Commute Use the results from Problem 25 in Section 4.1 and Problem 17 in Section 4.2 to: (a) Determine the coefficient of determination, R2. (b) Interpret the coefficient of
Use the results from Problem 26 in Section 4.1 and Problem 18 in Section 4.2 to: (a) Determine the coefficient of determination, R2. (b) Interpret the coefficient of determination and comment on
Use the results from Problem 27 in Section 4.1 and Problem 19 in Section 4.2 to: (a) Compute the coefficient of determination, R2. (b) Interpret the coefficient of determination and comment on the
Use the results from Problem 28 in Section 4.1 and Problem 20 in Section 4.2 to: (a) Compute the coefficient of determination, R2. (b) Interpret the coefficient of determination and comment on the
Use the results from Problem 29 in Section 4.1 and Problem 21 in Section 4.2. (a) What proportion of the variability in miles per gallon is explained by the relation between weight of the car and
Use the results from Problem 30 in Section 4.1 and Problem 22 in Section 4.2. (a) What proportion of the variability in the length of the right tibia is explained by the relation between the length
Suppose that we add the Dodge Viper to the data in Problem 21 in Section 4.2.A Dodge Viper weighs 3425 pounds and gets 11 miles per gallon. Compute the coefï¬cient of determination of
Suppose that we find a bear that is 205 cm tall and weighs 187 kg and add the bear to the data in Problem 20 from Section 4.2. Total Length (cm), x ..... Weight (kg), y 139.0
In Section 3.2, we introduced one measure of risk used by ï¬nancial analysts, the standard deviation of rate of return. In this problem we will learn about a second measure of risk of a stock,
The following data represent scores earned by students in Sullivan’s Elementary Algebra course for Chapter 2 (Linear Equations and Inequalities in One Variable) and Chapter 3 (Linear Equations and
What is meant by a marginal distribution? What is meant by a conditional distribution?
Refer to Table 8. Is constructing a conditional distribution by level of education different from constructing a conditional distribution by employment status? If they are different, explain the
(a) Construct a frequency marginal distribution.(b) Construct a relative frequency marginal distribution.(c) Construct a conditional distribution by x.(d) Draw a bar graph of the conditional
(a) Construct a frequency marginal distribution.(b) Construct a relative frequency marginal distribution.(c) Construct a conditional distribution by x.(d) Draw a bar graph of the conditional
In a recent Harris Poll, a random sample of adult Americans (18 years and older) was asked, “When you see an ad emphasizing that a product is ‘Made in America,’ are you more likely
In a recent Harris Poll, a random sample of adult Americans (18 years and older) was asked, “Given a choice of the following, which one would you most want to be?†Results of the survey,
Is there an association between party afï¬liation and gender? The following data represent the gender and party afï¬liation of registered voters based on a random sample of 802 adults.(a)
The Pew Research Center for the People and the Press conducted a poll in which it asked about the availability of abortion. The table is based on the results of the survey.(a) Construct a frequency
The General Social Survey asks questions about ones happiness and health. One would think that health plays a role in ones happiness. Use the data in the table to determine
The General Social Survey asks questions about one’s happiness in marriage. Is there an association between gender and happiness in marriage? Use the data in the table to determine if gender
Could it be that smoking actually increases survival rates among women? The following data represent the 20-year survival status and smoking status of 1314 English women who participated in a cohort
Researchers conducted a study to determine which of two treatments, A or B, is more effective in the treatment of kidney stones. The results of their experiment are given in the table.(a) Which
(a) Which among the following numbers could be the probability of an event?(b) Which among the following numbers could be the probability of an event?
Suppose that E = {yellow}. Compute the probability of Ec. Let the sample space be S = {red, green, blue, orange, yellow}. Suppose that the outcomes are equally likely.
Suppose that P(E) = 0.76, P(F ) = 0.45, and P(E and F ) = 0.32. What is P(E or F )? Let the sample space be S = {red, green, blue, orange, yellow}. Suppose that the outcomes are equally likely.
Suppose that P(E) = 0.36, P(F ) = 0.12, and E and F are mutually exclusive. What is P(E or F )?
Determine the value of each of the following: (a) 7! (b) 0! (c) 9C4 (d) 10C3 (e) 9P2 (f ) 12P4
In the game of roulette, a wheel consists of 38 slots, numbered 0, 00, 1, 2, . . . , 36. (See the photo in Problem 31 from Section 5.1.) To play the game, a metal ball is spun around the wheel and
In 2009, there were 33,722 traffic fatalities in the United States. Of these, 9817 were alcohol related. (a) What is the probability that a randomly selected traffic fatality in 2009 was alcohol
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.Age ......Number18–79
The following data represent the birth weights (in grams) of babies born in 2007, along with the period of gestation.(a) What is the probability that a randomly selected baby born in 2007 was
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
Pick 3 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
Pick 4 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).
Suppose that you draw 3 cards without replacement from a standard 52-card deck. What is the probability that all 3 cards are aces?
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
If four students enter a classroom that has 10 vacant seats, in how many ways can they be seated?
How many different vertical arrangements are there of 10 flags if 4 are white, 3 are blue, 2 are green, and 1 is red?
How many different simple random samples of size 8 can be obtained from a population whose size is 55?
In one of Arizona’s lotteries, balls are numbered 1 to 35. Five balls are selected randomly, without replacement. The order in which the balls are selected does not matter. To win, your numbers
Because of a mistake in packaging, a case of 12 bottles of red wine contained 5 Merlot and 7 Cabernet, each without labels. All the bottles look alike and have an equal probability of being chosen.
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
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
The following data represent the number of cases of coffee or ï¬lters sold by four sales reps in a recent sales competition.(a) What is the probability that a randomly selected case
Suppose that E = {Adam}. Compute the probability of Ec.
Suppose that P(E) = 0.37 and P(F) = 0.22. (a) Find P(E or F) if E and F are mutually exclusive. (b) Find P(E and F) if E and F are independent.
Suppose that P(E) = 0.15, P(F) = 0.45, and P(F|E) = 0.70. (a) What is P(E and F)? (b) What is P(E or F)? (c) What is P(E|F)? (d) Are E and F independent?
Determine the value of each of the following: (a) 8! (b) 12C6 (c) 14P8
Craps is a dice game in which two fair dice are cast. If the roller shoots a 7 or 11 on the first roll, he or she wins. If the roller shoots a 2, 3, or 12 on the first roll, he or she loses. (a)
The National Fire Protection Association reports that 32% of fires in 2006 were in structures. What is the probability that a randomly selected fire from 2006 was in a structure? What is the
The following probability model shows the distribution of the most-popular-selling Girl Scout Cookies. Cookie Type ..................................................... Probability Thin Mints
The following represent the results of a survey in which individuals were asked to disclose what they perceive to be the ideal number of children.(a) What is the probability an individual believes
During the 2010 season, the Minnesota Twins won 58% of their games. Assuming that the outcomes of the baseball games are independent and that the percentage of wins this season will be the same as in
You just received a shipment of 10 DVD players. One DVD player is defective. You will accept the shipment if two randomly selected DVD players work. What is the probability that you will accept the
In Pennsylvania’s Cash 5 lottery, balls are numbered 1 to 43. Five balls are selected randomly, without replacement. The order in which the balls are selected does not matter. To win, your numbers
A local area network requires eight characters for a password. The first character must be a letter, but the remaining seven characters can be either a letter or a digit (0 through 9). Lower- and
In 1 second, a 3-GHz computer processor can generate about 3 million passwords. How long would it take such a processor to generate all the passwords for the scheme in Problem 17?
How many distinguishable DNA sequences can be formed using two As, four Cs, four Gs, and five Ts?
A student is taking a 40-question multiple-choice test. Each question has ï¬ve possible answers. Since the student did not study for the test, he guesses on all the questions. Letting
Verify that the following is a probability model. What do we call the outcome “blue”? Color ..... Probability Red ...... 0.3 Green .... 0.15 Blue ..... 0 Brown ..... 0.15 Yellow .....
Verify that the following is a probability model. If the model represents the colors of M&Ms in a bag of milk chocolate M&Ms, explain what the model implies. Color ..... Probability Red
Why is the following not a probability model? Color ..... Probability Red ..... 0.1 Green ..... 0.1 Blue ..... 0.1 Brown ..... 0.4 Yellow ..... 0.2 Orange ..... 0.3
Which of the following numbers could be the probability of an event?
In five-card stud poker, a player is dealt five cards. The probability that the player is dealt two cards of the same value and three other cards of different value so that the player has a pair is
In seven-card stud poker, a player is dealt seven cards. The probability that the player is dealt two cards of the same value and five other cards of different value so that the player has a pair is
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