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Elementary Statistics 8th Edition Neil A. Weiss - Solutions
Following are the size and price data for custom homes from Exercise 4.52.a. Compute SST, SSR, and SSE, using Formula 4.2 on page 167. b. Compute the coefficient of determination, r2. c. Determine the percentage of variation in the observed values of the response variable explained by the
Following are the data on plant weight and quantity of volatile emissions from Exercise 4.53.a. Compute SST, SSR, and SSE, using Formula 4.2 on page 167.b. Compute the coefficient of determination, r2.c. Determine the percentage of variation in the observed values of the response variable explained
Following are the data on age and crown-rump length for fetuses from Exercise 4.54.a. Compute SST, SSR, and SSE, using Formula 4.2 on page 167.b. Compute the coefficient of determination, r2.c. Determine the percentage of variation in the observed values of the response variable explained by the
Following are the data on study time and score for calculus students from Exercise 4.55.a. Compute SST, SSR, and SSE, using Formula 4.2 on page 167.b. Compute the coefficient of determination, r2.c. Determine the percentage of variation in the observed values of the response variable explained by
The data from Exercise 4.64 for number of birdies during a tournament and final score for 63 women golfers are on the WeissStats CD.a. Decide whether finding a regression line for the data is reasonable. If so, then also do parts (b)–(d).b. Obtain the coefficient of determination.c. Determine the
The data from Exercise 4.65 for the ages at inauguration and of death for the presidents of the United States are on the WeissStats CD.a. Decide whether finding a regression line for the data is reasonable. If so, then also do parts (b)–(d).b. Obtain the coefficient of determination.c. Determine
The data from Exercise 4.66 for percentage of gross domestic product (GDP) spent on health care and life expectancy, in years, for selected countries are on the WeissStats CD. Do the required parts separately for each gender.a. Decide whether finding a regression line for the data is reasonable. If
The data from Exercise 4.68 for home size (in square feet) and assessed value (in thousands of dollars) for the same homes as in Exercise 4.97 are on the WeissStats CD.a. Decide whether finding a regression line for the data is reasonable. If so, then also do parts (b)–(d).b. Obtain the
The data from Exercise 4.69 for average high and low temperatures in January for a random sample of 50 cities are on the WeissStats CD.a. Decide whether finding a regression line for the data is reasonable. If so, then also do parts (b)–(d).b. Obtain the coefficient of determination.c. Determine
For each of the sums of squares in regression, state its name and what it measures. a. SST b. SSR c. SSE
Fill in the blanks. a. One use of the linear correlation coefficient is as a descriptive measure of the strength of the _________relationship between two variables. b. A positive linear relationship between two variables means that one variable tends to increase linearly as the other _________. c.
A small company has purchased a microcomputer system for $7200 and plans to depreciate the value of the equipment by $1200 per year for 6 years. Let x denote the age of the equipment, in years, and y denote the value of the equipment, in hundreds of dollars. a. Find the equation that expresses y in
Graduation rate-the percentage of entering freshmen attending full time and graduating within 5 years-and what influences it have become a concern in U.S. colleges and universities. U.S. News and World Report's "College Guide" provides data on graduation rates for colleges and universities as a
Refer to Problem 14.a. Determine SST, SSR, and SSE by using the computing formulas. b. Obtain the coefficient of determination. c. Obtain the percentage of the total variation in the observed graduation rates that is explained by student-to-faculty ratio (i.e., by the regression line). d. State how
Refer to Problem 14.a. Compute the linear correlation coefficient, r. b. Interpret your answer from part (a) in terms of the linear relationship between student-to-faculty ratio and graduation rate. c. Discuss the graphical implications of the value of the linear correlation coefficient, r. d. Use
Consider the linear equation y = 4 − 3x. a. At what y-value does its graph intersect the y-axis? b. At what x-value does its graph intersect the y-axis? c. What is its slope? d. By how much does the y-value on the line change when the x-value increases by 1 unit? e. By how much does the y-value
Answer true or false to each statement, and explain your answers. a. The y-intercept of a line has no effect on the steepness of the line. b. A horizontal line has no slope. c. If a line has a positive slope, y-values on the line decrease as the x-values decrease.
Fill in the blanks. a. Based on the least-squares criterion, the line that best fits a set of data points is the one having the possible sum of squared errors. b. The line that best fits a set of data points according to the least-squares criterion is called the _______line. c. Using a regression
In the context of regression analysis, what is an a. Outlier? b. Influential observation?
An ordinary deck of playing cards has 52 cards. There are four suits-spades, hearts, diamonds, and clubs-with 13 cards in each suit. Spades and clubs are black; hearts and diamonds are red. If one of these cards is selected at random, what is the probability that it is a. A spade? b. Red? c. Not
TheWorld Almanac provides information on past and projected total solar eclipses from 1955 to 2015. Unlike total lunar eclipses, observing a total solar eclipse from Earth is rare because it can be seen along only a very narrow path and for only a short period of time. a. Let X denote the duration,
Suppose that P(Z > 1.96) = 0.025. Find P(Z ≤ 1.96).
Suppose that T and Z are random variables. a. If P(T > 2.02) = 0.05 and P(T < −2.02) = 0.05, obtain P(−2.02 ≤ T ≤ 2.02). b. Suppose that P(−1.64 ≤ Z ≤ 1.64) = 0.90 and also that P(Z > 1.64) = P(Z < −1.64). Find P(Z > 1.64).
Let c > 0 and 0 ≤ α ≤ 1. Also let X, Y, and T be random variables. a. If P(X > c) = α, determine P(X ≤ c) in terms of α. b. If P(Y > c) = α/2 and P(Y < −c) = P(Y > c), obtain P(−c ≤ Y ≤ c) in terms of α. c. Suppose that P(−c ≤ T ≤ c) = 1 − α and, moreover, that P(T <
Refer to the probability distribution displayed in Table 5.11 on page 213.a. Use the technology of your choice to repeat the simulation done in Example 5.18 on page 213.b. Obtain the proportions for the number of heads in three tosses and compare them to the probability distribution in Table
Suppose that the random variables X and Y represent the amount of return on two different investments. Further suppose that the mean of X equals the mean of Y but that the standard deviation of X is greater than the standard deviation of Y.a. On average, is there a difference between the returns of
The random variable X is the crew size of a randomly selected shuttle mission between April 1981 and July 2000. Its probability distribution is as follows.a. Find and interpret the mean of the random variable.b. Obtain the standard deviation of the random variable by using one of the formulas given
The random variable Y is the number of persons living in a randomly selected occupied housing unit. Its probability distribution is as follows.a. Find and interpret the mean of the random variable.b. Obtain the standard deviation of the random variable by using one of the formulas given in
The random variable Y is the number of color television sets owned by a randomly selected household with annual income between $15,000 and $29,999. Its probability distribution is as follows.a. Find and interpret the mean of the random variable.b. Obtain the standard deviation of the random
A bowl contains 12 poker chips-3 red, 4 white, and 5 blue. If one of these poker chips is selected at random from the bowl, what is the probability that its color is a. Red? b. Red or white? c. Not white?
The random variable X is the number of girls of four children born to a couple that is equally likely to have either a boy or a girl. Its probability distribution is as follows.a. Find and interpret the mean of the random variable. b. Obtain the standard deviation of the random variable by using
The random variable Y is the sum of the dice when two balanced dice are rolled. Its probability distribution is as follows.a. Find and interpret the mean of the random variable.b. Obtain the standard deviation of the random variable by using one of the formulas given in Definition 5.10 on page
TheWorld Series in baseball is won by the first team to win four games (ignoring the 1903 and 1919€“1921 World Series, when it was a best of nine). As found on the Major League Baseball Web site in World Series Overview, historically, the lengths of the World Series are as given in the
An archer shoots an arrow into a square target 6 feet on a side whose center we call the origin. The outcome of this random experiment is the point in the target hit by the arrow. The archer scores 10 points if she hits the bull's eye-a disk of radius 1 foot centered at the origin; she scores 5
The Federal Communications Commission publishes a semiannual report on providers and services for Internet access titled High Speed Services for Internet Access. The report published in March 2008 included the following information on the percentage of zip codes with a specified number of
An American roulette wheel contains 38 numbers: 18 are red, 18 are black, and 2 are green. When the roulette wheel is spun, the ball is equally likely to land on any of the 38 numbers. Suppose that you bet $1 on red. If the ball lands on a red number, you win $1; otherwise you lose your $1. Let X
An investor plans to put $50,000 in one of four investments. The return on each investment depends on whether next year's economy is strong or weak. The following table summarizes the possible payoffs, in dollars, for the four investments. Let V, W, X, and Y denote the payoffs for the certificate
An insurance company wants to design a homeowner's policy for mid-priced homes. From data compiled by the company, it is known that the annual claim amount, X, in thousands of dollars, per homeowner is a random variable with the following probability distribution.a. Determine the expected annual
One method for deciding among various investments involves the concept of expected utility. Economists describe the importance of various levels of wealth by using utility functions. For instance, in most cases, a single dollar is more important (has greater utility) for someone with little wealth
A factory manager collected data on the number of equipment breakdowns per day. From those data, she derived the probability distribution shown in the following table, where W denotes the number of breakdowns on a given day.a. Determine μW and ÏW. b. On average, how many
Reporter D. McGinn discussed the changing demographics for successful chief executive officers (CEOs) of America's top companies in the article, "Fresh Ideas" (Newsweek, June 13, 2005, pp. 42-46). The following frequency distribution reports the highest education level achieved by Standard and
Let X be the value of a randomly selected decimal digit, that is, a whole number between 0 and 9, inclusive. a. Use simulation to estimate the mean of X. Explain your reasoning. b. Obtain the exact mean of X by applying Definition 5.9 on page 217. Compare your result with that in part (a).
Benny's Barber Shop in Cleveland has five chairs for waiting customers. The number of customers waiting is a random variable Y with the following probability distribution.a. Compute and interpret the mean of the random variable Y . b. In a large number of independent observations, how many
Let X be a discrete random variable with a finite number of possible values, say, x1, x2, . . . , xm. For convenience, set pk = P(X = xk ), for k = 1, 2, . . . ,m. Think of a horizontal axis as a seesaw and each pk as a mass placed at point xk on the seesaw. The center of gravity of these masses is
Give two examples of Bernoulli’s trails other than those presented in the text.
Determine the value of each of the following binomial co-efficientsa.b.c.d.
Evaluate the following binomial coefficients(a)(b) (c)(d)
In the journal article "The 2003-2004 Russian Elections and Prospects for Democracy" (Europe-Asia Studies, Vol. 57, No. 3, pp. 369-398), R. Sakwa examined the fourth electoral cycle that independent Russia entered in 2003. The following frequency table lists the candidates and numbers of votes from
n = 4, p = 0.3, P(X = 2)a. The binomial probability formula, Formula 5.4 Round your probability answers to three decimal places.b. Table VII in Appendix A. Compare your answer here to that in part (a).
n = 5, p = 0.6, P(X = 3) a. The binomial probability formula, Formula 5.4 Round your probability answers to three decimal places. b. Table VII in Appendix A. Compare your answer here to that in part (a).
From the Florida State Center for Health Statistics report Women and Cardiovascular Disease Hospitalization, we obtained the following table showing the number of female hospitalizations for cardiovascular disease, by age group, during one year. Age group (yr) Number 0–19
If we repeatedly toss a balanced coin, then, in the long run, it will come up heads about half the time.But what is the probability that such a coin will come up heads exactly half the time in 10 tosses?
If we repeatedly roll a balanced die, then, in the long run, it will come up "4" about one-sixth of the time. But what is the probability that such a die will come up "4" exactly once in six rolls?
According to the Daily Racing Form, the probability is about 0.67 that the favorite in a horse race will finish in the money (first, second, or third place). In the next five races, what is the probability that the favorite finishes in the moneya. Exactly twice? b. Exactly four times?c. At least
The probability is 0.314 that the gestation period of a woman will exceed 9 months. In six human births, what is the probability that the number in which the gestation period exceeds 9 months isa. Exactly three?b. Exactly five?c. At least five?d. Between three and five, inclusive?e. Determine the
The National Safety Council publishes information about automobile accidents in Accident Facts. According to that document, the probability is 0.40 that a traffic fatality will involve an intoxicated or alcoholimpaired driver or nonoccupant. In eight traffic fatalities, find the probability that
A student takes a multiple-choice exam with 10 questions, each with four possible selections for the answer. A passing grade is 60% or better. Suppose that the student was unable to find time to study for the exam and just guesses at each question. Find the probability that the studenta. Gets at
J. Fetto, in the article "Love Stinks" (American Demographics, Vol. 25, No. 1, pp. 10-11), reports that Americans split with their significant other for many reasons-including indiscretion, infidelity, and simply "growing apart." According to the article, 35% of American adults have experienced a
The U.S. Census Bureau publishes data on housing units in American Housing Survey for the United States. The following table provides a frequency distribution for the number of rooms in U.S. housing units. The frequencies are in thousands. Rooms No. of units 1 ........... 637 2
An article titled "You're Eating That?", published in the New York Times, discussed consumer perception of food safety. The article cited research by the Food Marketing Institute, which indicates that 66% of consumers in the United States are confident that the food they buy is safe. Suppose that
According to the Centers for Disease Control and Prevention publication Health, United States, in 2002, 16.5% of persons under the age of 65 had no health insurance coverage. Suppose that, today, four persons under the age of 65 are randomly selected.a. Assuming that the uninsured rate is the same
In the Scientific American article "Reducing Crime: Rehabilitation is Making a Comeback," R. Doyle examined rehabilitation of felons. One aspect of the article discussed recidivism of juvenile prisoners between 14 and 17 years old, indicating that 82% of those released in 1994 were rearrested
A success, s, in Bernoulli trials is often derived from a collection of outcomes. For example, an American roulette wheel consists of 38 numbers, of which 18 are red, 18 are black, and 2 are green. When the roulette wheel is spun, the ball is equally likely to land on any one of the 38 numbers. If
A previous Arizona state lottery called Lotto is played as follows: The player selects six numbers from the numbers 1-42 and buys a ticket for $1. There are six winning numbers, which are selected at random from the numbers 1-42. To win a prize, a Lotto ticket must contain three or more of the
Sickle cell anemia is an inherited blood disease that occurs primarily in blacks. In the United States, about 15 of every 10,000 black children have sickle cell anemia. The red blood cells of an affected person are abnormal; the result is severe chronic anemia (inability to carry the required
A sales representative for a tire manufacturer claims that the company's steel-belted radials last at least 35,000 miles. A tire dealer decides to check that claim by testing eight of the tires. If 75% or more of the eight tires he tests last at least 35,000 miles, he will purchase tires from the
From past experience, the owner of a restaurant knows that, on average, 4% of the parties that make reservations never show. How many reservations can the owner accept and still be at least 80% sure that all parties that make a reservation will show?
Refer to the discussion on the binomial approximation to the hypergeometric distribution that begins on page 230. a. If sampling is with replacement, explain why the trials are independent and the success probability remains the same from trial to trial-always the proportion of the population that
Following is a gender frequency distribution for students in Professor Weiss's introductory statistics class. Gender Frequency Male .......... 17 Female ......... 23 Two students are selected at random. Find the probability that both students are male if the selection is done a. With
As reported by the Federal Bureau of Investigation in Crime in the United States, the age distribution of murder victims between 20 and 59 years old is as shown in the following table. Age (yr) Frequency 20–24 ........ 2834 25–29 ........ 2262 30–34 ........ 1649 35–39
In this exercise, we discuss the hypergeometric distribution in more detail. When sampling is done without replacement from a finite population, the hypergeometric distribution is the exact probability distribution for the number of members sampled that have a specified attribute. The
In this exercise, we discuss the geometric distribution, the probability distribution for the number of trials until the first success in Bernoulli trials. The geometric probability formula is P(X = x) = p(1 − p)x−1, where X denotes the number of trials until the first success and p the success
Another important discrete probability distribution is the Poisson distribution, named in honor of the French mathematician and physicist Simeon Poisson (1781-1840). This probability distribution is often used to model the frequency with which a specified event occurs during a particular period of
The population of Seoul was studied in an article by B. Lee and J. McDonald, "Determinants of Commuting Time and Distance for Seoul Residents: The Impact of Family Status on the Commuting of Women" (Urban Studies, Vol. 40, No. 7, pp. 1283-1302). The authors examined the different occupations for
From Aneki.com, an independent, privately operated Web site based in Montreal, Canada, which is dedicated to promoting wider knowledge of the world's countries and regions, we obtained a frequency distribution of the number of Nobel Prize winners, by country. Country Winners United
According to Survey of Graduate Science Engineering Students and Postdoctorates, published by the U.S. National Science Foundation, the distribution of graduate science students in doctorate-granting institutions is as follows. Frequencies are in thousands. Field
Concerning the equal-likelihood model of probability, a. What is it? b. How is the probability of an event found?
A family is defined to be a group of two or more persons related by birth, marriage, or adoption and residing together in a household. According to Current Population Reports, published by the U.S. Census Bureau, the size distribution of U.S. families is as follows. Frequencies are in thousands.
Two balanced dice are rolled. Refer to Fig. 5.1 on page 187 and determine the probability that the sum of the dice isIN FIGUREa. 6. b. even. c. 7 or 11. d. 2, 3, or 12.
A balanced dime is tossed three times. The possible outcomes can be represented as follows.Here, for example, HHT means that the first two tosses come up heads and the third tails. Find the probability that a. Exactly two of the three tosses come up heads. b. The last two tosses come up tails. c.
Refer to Exercise 5.15. Rooms No. of units 1 ........... 637 2 ........... 1,399 3 ........... 10,941 4 ........... 22,774 5 ........... 28,619 6 ........... 25,325 7 ........... 15,284 8+ ......... 19,399 a. Which, if any, of the events in parts (a)-(e) are certain? impossible? b.
Refer to Exercise 5.20. a. Which, if any, of the events in parts (a)-(e) are certain? impossible? b. Determine the probability of each event identified in part (a).
Use the frequentist interpretation of probability to interpret each of the following statements. a. The probability is 0.314 that the gestation period of a woman will exceed 9 months. b. The probability is 0.667 that the favorite in a horse race will finish in the money (first, second, or third
Refer to Exercise 5.26. a. In 4000 human gestation periods, roughly how many will exceed 9 months? b. In 500 horse races, roughly how many times will the favorite finish in the money? c. In 389 traffic fatalities, roughly how many will involve an intoxicated or alcohol-impaired driver or
In 2008, according to the National Governors Association, 22 of the state governors were Republicans. Suppose that on each day of 2008, one U.S. state governor was randomly selected to read the invocation on a popular radio program. On approximately how many of those days should we expect that a
At a certain university in the United States, 62% of the students are at least bilingual- speaking English and at least one other language. Of these students, 80% speak Spanish and, of the 80% who speak Spanish, 10% also speak French. Determine the probability that a randomly selected student at
Consider the random experiment of tossing a coin once. There are two possible outcomes for this experiment, namely, a head (H) or a tail (T).a. Repeat the random experiment five times-that is, toss a coin five times-and record the information required in the following table. (The third and fourth
As found in USA TODAY, results of a survey by International Communications Research revealed that roughly 75% of adult women believe that a romantic relationship over the Internet while in an exclusive relationship in the real world is cheating. What are the odds against randomly selecting an adult
Funny Cide, winner of both the 2003 Kentucky Derby and the 2003 Preakness Stakes, was the even-money (1-to-1 odds) favorite to win the 2003 Belmont Stakes and thereby capture the coveted Triple Crown of thoroughbred horseracing. The second favorite and actual winner of the 2003 Belmont Stakes,
A study was conducted by the firm Coleman & Associates, Inc. to determine who curses at their computer. The results, which appeared in USA TODAY, indicated that 46% of people age 18-34 years have cursed at their computer. What are the odds against a randomly selected 18- to 34-year-old having
An issue of Travel + Leisure Golf magazine (May/June, 2005, p. 36) reported several facts about lightning. Here are three of them. The odds of an individual being struck by lightning in a year in the United States are about 280,000 to 1 (against). The odds of an individual being struck by
Construct a Venn diagram representing each event. a. (not E) b. (A or B) c. (A & B) d. (A & B & C) e. (A or B or C) f. ((not A) & B)
What does it mean for two events to be mutually exclusive? For three events?
Answer true or false to each statement, and give reasons for your answers. a. If event A and event B are mutually exclusive, so are events A, B, and C for every event C. b. If event A and event B are not mutually exclusive, neither are events A, B, and C for every event C.
A committee consists of five executives, three women and two men. Their names are Maria (M), John (J), Susan (S), Will (W), and Holly (H). The committee needs to select a chairperson and a secretary. It decides to make the selection randomly by drawing straws. The person getting the longest straw
When a dime is tossed four times, there are the following 16 possible outcomes.Here, for example, HTTH represents the outcome that the first toss is heads, the next two tosses are tails, and the fourth toss is heads. List the outcomes constituting each of the following four events. A = event
Refer to Exercise 5.41. For each of the following events, list the outcomes that constitute the event and describe the event in words.a. (not A) b. (A & B) c. (B or C)
Refer to Exercise 5.42. For each of the following events, list the outcomes that constitute the event and describe the event in words.a. (not C) b. (C & D) c. (A or C)
Refer to Exercise 5.43. For each of the following events, list the outcomes that constitute the event, and describe the event in words.a. (not A) b. (B & D) c. (B or C)
Refer to Exercise 5.44. For each of the following events, list the outcomes that constitute the event, and describe the event in words.a. (not B) b. (A & B) c. (C or D)
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