Regarding the equal-likelihood model, a. what is it? b. how are probabilities computed?
> For the standard normal curve, find the z-score(s) a. that has area 0.30 to its left. b. that has area 0.10 to its right. c. z0.025, z0.05, z0.01, and z0.005. d. that divide the area under the curve into a middle 0.99 area and two outside 0.005 areas.
> Determine and sketch the area under the standard normal curve that lies a. to the left of −3.02. b. to the right of 0.61. c. between 1.11 and 2.75. d. between −2.06 and 5.02. e. between −4.11 and −1.5. f. either to the left of 1 or to the right of 3.
> According to Table II, the area under the standard normal curve that lies to the left of 1.05 is 0.8531. Without further reference to Table II, determine the area under the standard normal curve that lies a. to the right of 1.05. b. to the left of −1.05
> Sketch the normal curve having the parameters a. μ = −1 and σ = 2. b. μ = 3 and σ = 2. c. μ = −1 and σ = 0.5.
> Assume that the variable under consideration has a density curve. Note that the answers required here may be only approximately correct. The percentage of all possible observations of a variable that lie between 25 and 50 equals the area under its densit
> If you observe the values of a normally distributed variable for a sample, a normal probability plot should be roughly .
> Roughly speaking, what are the normal scores corresponding to a sample of observations?
> For data that are grouped in classes based on more than a single value, lower class limits (or cutpoints) are used on the horizontal axis of a histogram for depicting the classes. Class marks (or midpoints) can also be used, in which case each bar is cen
> State the empirical rule for variables.
> What does the symbol zα signify?
> Explain how to use Table II to determine the z-score that has a specified area to its a. left under the standard normal curve. b. right under the standard normal curve.
> Explain how to use Table II to determine the area under the standard normal curve that lies a. to the left of a specified z-score. b. to the right of a specified z-score. c. between two specified z-scores.
> What key fact permits you to determine percentages for a normally distributed variable by first converting to z-scores and then determining the corresponding area under the standard normal curve?
> Consider the normal curves that have the parameters μ = 1.5 and σ = 3; μ = 1.5 and σ = 6.2; μ = −2.7 and σ = 3; μ = 0 and σ = 1. a. Which curve has the largest spread? b. Which curves are centered at the same place? c. Which curves have the same spread?
> Answer true or false to each statement. Explain your answers. a. Two normal distributions that have the same mean are centered at the same place, regardless of the relationship between their standard deviations. b. Two normal distributions that have the
> Identify the distribution of the standardized version of a normally distributed variable.
> What is a density curve, and why are such curves important?
> Identify one reason why the complementation rule is useful.
> Of the variables you have studied so far, which type yields non numerical data?
> Answer true or false to each statement and explain your answers. a. For any two events, the probability that one or the other of the events occurs equals the sum of the two individual probabilities. b. For any event, the probability that it occurs equals
> Suppose that E is an event. Use probability notation to represent a. the probability that event E occurs. b. the probability that event E occurs is 0.436.
> What does it mean for two or more events to be mutuallyexclusive?
> Identify a commonly used graphical technique for portraying events and relationships among events.
> Refer to Problem 40. a. Draw a probability histogram for the random variable X. b. The selection of the four households was done without replacement. Strictly speaking, then, why is the probability distribution that you obtained in Problem 40(b) only app
> According to JAVMA News, a publication of the American Veterinary Medical Association, roughly 60% of U.S. households own one or more pets. Four U.S. households are selected at random. Use Table VII in Appendix A to solve the following problems. a. Find
> Decide which of these numbers could not possibly be probabilities. Explain your answers. a. 0.047 b. −0.047 c. 3.5 d. 1/3.5
> In the game of soccer, a penalty kick is a direct free kick, taken from 12 yards out from the goal on the penalty mark. According to the article “Penalty Kicks in Soccer: An Empirical Analysis of Shooting Strategies and Goalkeeper’s Preferences” (Soccer
> Use the binomial probability formula. Compare your results.
> Refer to the probability distribution displayed in the table in Problem 36. a. Find the mean of the random variable Y . b. On average, how many lines are busy? c. Compute the standard deviation of Y . d. Construct a probability histogram for Y ; locate t
> Explain the advantages and disadvantages of frequency histograms versus frequency distributions.
> An accounting office has six incoming telephone lines. The probability distribution of the number of busy lines, Y, is as follows. Use random-variable notation to express each of the following events. The number of busy lines is a. exactly four. b. at le
> According to the Arizona State University Enrollment Summary, a frequency distribution for the number of undergraduate students attending Arizona State University (ASU) in the Fall 2012 semester, by class level, is as shown in the following table. Here,
> Consider the events (not J ), (H & I), (H or K), and (H & K) discussed in Problem 31. a. Find the probability of each of those four events, using the f/N rule. b. Compute P(J ), using the complementation rule and your answer for P(not J ) from part (a).
> Refer to Problems 30 and 31. a. Use the second column of Table 5.21 and the f/N rule to compute the probability of each of the events H, I, J, and K. b. Express each of the events H, I, J , and K in terms of the mutually exclusive events displayed. c. Co
> For the following groups of events, determine which are mutually exclusive. a. H and I b. I and K c. H and (not J ) d. H, (not J ), and K
> A federal individual income tax return is selected at random. Let H = event the return shows an AGI between $20K and $100K, I = event the return shows an AGI of less than $50K, J = event the return shows an AGI of less than $100K, and K = event the retur
> The Internal Revenue Service compiles data on income tax returns and summarizes its findings in Statistics of Income. The first two columns of Table 5.21 show a frequency distribution (number of returns) for adjusted gross income (AGI) from federal indiv
> What meaning is given to the probability of an event by the frequentist interpretation of probability?
> The Television Bureau of Advertising publishes a report titled TV Basics for the purpose of providing information to help advertisers make the most effective and efficient use of local and national spot television advertisements. The following table give
> Name three common discrete probability distributions other than the binomial distribution.
> Explain the difference between a frequency histogram and a relative-frequency histogram.
> Suppose that a simple random sample of size n is taken from a finite population in which the proportion of members having a specified attribute is p. Let X be the number of members sampled that have the specified attribute. a. If the sampling is done wit
> The following are two probability histograms of binomial distributions. For each, specify whether the success probability is less than, equal to, or greater than 0.5.
> The game of craps is played by rolling two balanced dice. A first roll of a sum of 7 or 11 wins; and a first roll of a sum of 2, 3, or 12 loses. To win with any other first sum, that sum must be repeated before a sum of 7 is thrown. It can be shown that
> In 10 Bernoulli trials, how many outcomes contain exactly three successes?
> What is the relationship between Bernoulli trials and the binomial distribution?
> List the three requirements for repeated trials of an experiment to constitute Bernoulli trials.
> Determine the value of each binomial coefficient.
> Determine 0!, 3!, 4!, and 7!.
> Two random variables, X and Y , have standard deviations 2.4 and 3.6, respectively. Which one is more likely to take a value close to its mean? Explain your answer.
> We used slightly different methods for determining the “middle” of a class with limit grouping and cutpoint grouping. Identify the methods and the corresponding terminologies.
> A random variable X has mean 3.6. If you make a large number of repeated independent observations of the random variable X, the average value of those observations will be approximately ___.
> A random variable X equals 2 with probability 0.386. a. Use probability notation to express that fact. b. If you make repeated independent observations of the random variable X, in approximately what percentage of those observations will you observe the
> If you sum the probabilities of the possible values of a discrete random variable, the result always equals ___.
> How do you graphically portray the probability distribution of a discrete random variable?
> What does the probability distribution of a discrete random variable tell you?
> Fill in the blanks. a. A is a quantitative variable whose value depends on chance___. b. A discrete random variable is a random variable whose possible values ____.
> A and B are events such that P(A) = 0.2, P(B) = 0.6, and P(A & B) = 0.1. Find P(A or B).
> E is an event and P(not E) = 0.4. Find P(E).
> A, B, and C are mutually exclusive events such that P(A) = 0.2, P(B) = 0.6, and P(C) = 0.1. Find P(A or B or C).
> Why is probability theory important to statistics?
> For quantitative data, we examined three types of grouping: single-value grouping, limit grouping, and cut point grouping. For each type of data given, decide which of these three grouping types is usually best. Explain your answers. a. Continuous data d
> In an on-line press release, ABCNews.com reported that “. . . 73 percent of Americans. . . favor a law that would require every gun sold in the United States to be test-fired first, so law enforcement would have its fingerprint in case it were ever used
> Based on the least-squares criterion, the line that best fits a set of data points is the one with the ____ possible sum of squared errors.
> Regarding the variables in a regression analysis, a. what is the independent variable called? b. what is the dependent variable called?
> Identify one use of a regression equation.
> What kind of plot is useful for deciding whether finding a regression line for a set of data points is reasonable?
> Explain your answers. If a line has a positive slope, y-values on the line decrease as the x-values decrease.
> Explain your answers. A horizontal line has no slope.
> Explain your answers. The y-intercept of a line has no effect on the steepness of the line.
> From the website Golf.com, part of Sports Illustrated Sites, we obtained the scores for the first and second rounds of the 2013 U.S. Open golf tournament. You will find those scores on the WeissStats site. For part (d), predict the second-round score of
> The National Oceanic and Atmospheric Administration publish temperature and precipitation information for cities around the world in Climates of the World. Data on average high temperature (in degrees Fahrenheit) in July and average precipitation (in inc
> From the International Data Base, published by the U.S. Census Bureau, we obtained data on infant mortality rate (IMR) and life expectancy (LE), in years, for a sample of 60 countries. The data are presented on the WeissStats site. For part (d), predict
> With regard to grouping quantitative data into classes in which each class represents a range of possible values, we discussed two methods for depicting the classes. Identify the two methods and explain the relative advantages and disadvantages of each m
> In the article “Effects of Human Population, Area, and Time on Non-native Plant and Fish Diversity in the United States” (Biological Conservation, Vol. 100, No. 2, pp. 243–252), M. McKinney investigated the relationship of various factors on the number o
> Refer to Problem 21. 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
> Refer to Problem 21. 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 rati
> Graduation rate—the percentage of entering freshmen attending full time and graduating within 5 years— and what influences it is a concern in U.S. colleges and universities. U.S. News and World Report’s “College Guide” provides data on graduation rates f
> A small company has purchased a computer 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.
> 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 b
> Answer true or false to the following statement, and explain your answer: A strong correlation between two variables doesn’t necessarily mean that they’re causally related.
> A value of r close to ____ suggests at most a weak linear relationship between the variables.
> A value of r close to −1 suggests a strong ____ linear relationship between the variables.
> A positive linear relationship between two variables means that one variable tends to increase linearly as the other ____ .
> State three of the most important guidelines in choosing the classes for grouping a quantitative data set.
> One use of the linear correlation coefficient is as a descriptive measure of the strength of the ____ relationship between two variables.
> For each of the sums of squares in regression, state its name and what it measures. a. SST b. SSR c. SSE
> Identify a use of the coefficient of determination as a descriptive measure.
> In the context of regression analysis, what is an a. outlier? b. influential observation?
> Using a regression equation to make predictions for values of the predictor variable outside the range of the observed values of the predictor variable is called _____ .
> The line that best fits a set of data points according to the least squares criterion is called the ____ line.
> For a linear equation y = b0 + b1x, identify the a. independent variable. b. dependent variable. c. slope. d. y-intercept.
> A quantitative data set of size 87 has mean 80 and standard deviation 10. At least how many observations lie between 60 and 100?
> What does Chebyshev’s rule say about the percentage of observations in any data set that lie within a. six standard deviations to either side of the mean? b. 1.5 standard deviations to either side of the mean?
> Complete the statement: Almost all the observations in any data set lie within ____ standard deviations to either side of the mean.
> Do the concepts of class limits, marks, cutpoints, and midpoints make sense for qualitative data? Explain your answer
> Data Set A has more variation than Data Set B. Decide which of the following statements are necessarily true. a. Data Set A has a larger mean than Data Set B. b. Data Set A has a larger standard deviation than Data Set B.
> Specify the mathematical symbol used for each of the following descriptive measures. a. Sample mean b. Sample standard deviation c. Population mean d. Population standard deviation
> Identify the most appropriate measure of variation corresponding to each of the following measures of center. a. Mean b. Median
> Philosophical and health issues are prompting an increasing number of Taiwanese to switch to a vegetarian lifestyle. In the paper “LDL of Taiwanese Vegetarians Are Less Oxidizable than Those of Omnivores” (Journal of Nutrition, Vol. 130, pp. 1591–1596),
