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# Statistics Final Test

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By McGraw-Hill Professional
Updated on Sep 13, 2011

## Statistics Final Test

You may draw diagrams or use a calculator if necessary. A good score is at least 75 correct.

1. The term empirical probability refers to
1. the probability of something going wrong in an experiment
2. the probability of a certain outcome, based on experience or observation
3. the probability that an experiment accurately represents real life
4. the probability that a certain event took place sometime in the past
5. the probability that a certain event is taking place right now
2. In a statistical distribution, the variance is
1. a measure of the extent to which the values are spread out
2. a measure of the correlation between the variables
3. an expression of the difference between the mean and the median
4. the distance of the mode from the center of the distribution
5. a measure of experimental error
3. Suppose q and r are both positive integers. Imagine a set of q items taken r at a time in a specific order. The possible number of permutations in this situation is symbolized qPr and can be calculated as follows:
qPr = q! / (qr)!
4. According to this formula, what is the number of possible permutations of 5 objects taken 3 at a time?

1. 10
2. 20
3. 60
4. 120
5. Table Exam-1 shows the results of a hypothetical experiment in which a 6-sided die is tossed 6000 times. What, if anything, is wrong with this table?
1. There is nothing wrong with the table; it is entirely plausible.
2. The data for the absolute frequency and the cumulative absolute frequency are in the wrong columns.
3. There is no way a coincidence like this could ever occur.
4. The absolute frequency values don't add up right.
5. The cumulative absolute frequency values don't add up right.
6. If a 6-sided die is tossed 6000 times and the results turn out like those shown in Table Exam-1, it is reasonable to conclude that
1. the die is biased or ''weighted''
2. the die is not biased or ''weighted''
3. the sampling frame is too large
4. the mean is equal to 0
5. the mode is equal to 0
7. Suppose q and r are both positive integers. Imagine a set of q items taken r at a time in no particular order. The possible number of combinations in this situation is symbolized qCr and can be calculated as follows:
qCr = q! / [r!(qr)!]
8. According to this formula, what is the number of possible combinations of 5 objects taken 3 at a time?

1. 10
2. 20
3. 60
4. 120
9. What is the arithmetic mean, or average, of a group of numbers represented by the variables t, u, v, and w?
1. (t + u + v + w) / 4
2. tuvw / 4
3. (t + u + v + w) / tuvw
4. tuvw / (t + u + v + w)
5. There is no way to express it without knowing actual number values.
10. Figure Exam-1 is an example of
1. a histogram
2. a pie graph
3. a bar graph
4. a pizza graph
5. a tablet graph
11. What is the angle at the apex (or central ''point'') of the wedge corresponding to 34.0% in Fig. Exam-1, to the nearest degree?
1. 34°
2. 56°
3. 122°
4. 244°
12. Imagine the set of all people in the world who read and write English. Call this set E. Now imagine the set of all people in the world. Call this set W. What can we say about the relationship between these two sets?
1. E is a subset of W.
2. E is an element of W.
3. W is a subset of E.
4. W is an element of E.
5. None of the above
13. Figure Exam-2 shows the letter-grade results of a hypothetical test given to a large group of students. This illustration is an example of
1. a horizontal bar graph
2. a fixed-width histogram
3. a variable-width histogram
4. a pie graph
5. a nomograph
14. What, if anything, is technically wrong with Fig. Exam-2?
1. The rectangles are not the correct heights to correspond to the percentages shown at the right.
2. The rectangles' widths don't reasonably represent the proportion of students receiving each letter grade.
3. The percentages don't add up correctly.
4. No teacher would ever give such a large proportion of students low grades.
5. Nothing is technically wrong with Fig. Exam-2.
15. Fill in the blank to make the following sentence true: ''The _____ of a particular outcome is the number of times it occurs within a specific sample of a population.''
1. frequency
2. variability
3. variance
4. standard deviation
5. distribution
16. Table Exam-2 illustrates the results of a test given to a group of students. What, if anything, is wrong or implausible with this table?
1. The percentages don't add up right.
2. The entries in the letter-grade column are listed upside-down.
3. The absolute frequency numbers don't correspond to the correct percentages.
4. It's impossible to tell how many students there are.
5. Nothing is wrong or implausible with this table.
17. Suppose you are told to calculate the probability of a certain event, and it turns out as P = 0.78544. What is this expressed as a percentage P%, rounded off to the nearest percentage point?
1. 0.78%
2. 0.79%
3. 78%
4. 79%
18. Fill in the blank to make the following sentence correct: ''A specific, well-defined characteristic of a population is called a _____ of that population.''
1. variable
2. mean
3. parameter
4. distribution
5. central limit
19. A continuous variable can attain any value between certain limits, but a discrete variable can attain
1. only one value
2. only the values of the limits themselves
3. only specific values
4. no values at all
5. only values that produce a straight-line graph
20. The set of all possible outcomes in an experiment is called
1. the variance
2. the sample space
3. the area under the curve
4. the normal distribution
5. the total probability
21. An error in an experiment can be caused by
1. imprecise visual interpolation of an instrument reading
2. proper tallying of the data
3. a machine that is working properly
4. rendering of the data in the form of a graph
5. any of the above
22. In a normal distribution, the Z score is a quantitative measure of the position of a particular element with respect to
1. the mean
2. the median
3. the mode
4. the standard deviation
5. the variance
23. Suppose you take a test with 100 questions, and you get a score of 77. Which, if any, of the following statements (a), (b), (c), or (d) can you make with certainty?
1. You scored in the 77th percentile.
2. You scored in the 78th percentile.
3. You scored in the 7th decile.
4. You scored in the 3rd quartile.
5. You can't make any of the above statements (a), (b), (c), or (d) with certainty.
24. Suppose you are analyzing a normal distribution. You have good estimates of the mean and standard deviation. Which of the following can be determined on the basis of this information?
1. The 50% confidence interval.
2. The 60% confidence interval.
3. The 70% confidence interval.
4. The 80% confidence interval.
5. All of the above (a), (b), (c), and (d) can be determined on the basis of this information.
25. Suppose you want to determine the percentage of people in your county who swim more than 1000 meters a day. Which of the following samples should you expect would be the best (least biased)?
1. All the people in the county over age 75.
2. All the hospital patients in the county.
3. All the people in the county who were born in August.
4. All the high-school students in the county.
5. All the people in the county who weigh less than 100 pounds.
26. As the width of the confidence interval in a normal distribution increases, the probability of a randomly selected element falling within that interval
1. approaches 68%
2. approaches 50%
3. increases
4. decreases
5. does not change
27. Suppose you buy a certificate of deposit (CD) at your bank. Once you've bought it, you leave it alone, allowing it to mature automatically and earn interest indefinitely. The value of this CD, in dollars, can be plotted against time, and the result is a function. Assuming the CD never loses value (the interest never becomes negative), this function is
1. nonincreasing
2. nondecreasing
3. linear
4. point-to-point
5. a histogram
28. An exclamation mark (!) following a positive whole number represents
1. the factorial
2. the mean
3. the median
4. the mode
5. the cumulative frequency
29. Refer to Fig. Exam-3. In this graph, the stock price is the
1. independent variable
2. dependent variable
3. mean
4. standard deviation
5. variance
30. In Fig. Exam-3, how might a statistician attempt to fill in the gap in the data, even if no actual data is available?
1. By means of linear extrapolation.
2. By finding the least-squares line.
3. By constructing a histogram.
4. By means of linear interpolation.
5. By invoking the law of averages.
31. The bias in an experiment can be minimized by
1. minimizing the number of samples
2. proper choice of the sampling frame
3. choosing a small population
4. using properly calibrated measuring equipment
5. all of the above
32. Which of the following is implied by the Central Limit Theorem?
1. As the size of a population increases beyond 30, the mean approaches the median.
2. As the size of a population increases beyond 30, the median approaches the mode.
3. If the sample size is 30 or more, then the sampling distribution of means is essentially a normal distribution.
4. In a bimodal distribution, the mean is always the same as the median if the population is 30 or more.
5. In a bimodal distribution, the mean approaches the median as the size of the population increases beyond 30.
33. Which of the following statements is true?
1. Two sets can be proper subsets of each other.
2. Two sets can be elements of each other.
3. The union of two sets is always at least as big as the smaller one.
4. The intersection of two sets is always at least as big as the smaller one.
5. The intersection of two sets can never be the same as their union.
34. In Fig. Exam-4, the sampling frame
1. coincides with the sample
2. is a subset of the sample
3. coincides with the population
4. is a subset of the population
5. is too small
35. When we draw specific conclusions on the basis of data and hypotheses, we are performing
1. linear interpolation
2. curve fitting
3. statistical inference
4. least-squares analysis
5. correlation determination
36. Percentiles divide a large data set into intervals, each interval containing 1% of the elements in the set. The percentile points represent the boundaries where the intervals meet. How many possible percentile points are there?
1. 4
2. 24
3. 25
4. 99
5. 100
37. Imagine that 2020 people take a 100-question test. Suppose 20 students get 100 correct answers, 20 students get 99 correct, 20 students get 98 correct, and so on, all the way down to 20 students getting none correct. For every possible test score, 20 students get that score. What is the mean score, accurate to two decimal places?
1. 49.55
2. 50.00
3. 50.45
4. 0
5. It cannot be defined.
38. Imagine that 2020 people take a 100-question test. Suppose 20 students get 100 correct answers, 20 students get 99 correct, 20 students get 98 correct, and so on, all the way down to 20 students getting none correct. For every possible test score, 20 students get that score. What is the mode score, accurate to two decimal places?
1. 49.55
2. 50.00
3. 50.45
4. 0
5. It cannot be defined.
39. Imagine that 2020 people take a 100-question test. Suppose 20 students get 100 correct answers, 20 students get 99 correct, 20 students get 98 correct, and so on, all the way down to 20 students getting none correct. For every possible test score, 20 students get that score. What is the median score, accurate to two decimal places?
1. 49.55
2. 50.00
3. 50.45
4. 0
5. It cannot be defined.
40. Let x be a discrete random variable that can attain n possible values, all equally likely. Suppose an outcome H results from exactly m different values of x, where mn. Then m/n represents
1. the empirical probability that H will result from any given value of x
2. the mathematical probability that H will result from any given value of x
3. the discrete probability that H will result from any given value of x
4. the continuous probability that H will result from any given value of x
5. none of the above
41. Suppose you take a standardized test. The teacher says you scored in the 4th percentile. You ask, ''What is the highest-scoring percentile?'' The teacher replies, ''The 1st.'' Based on this, you can be certain that you scored
1. in the highest 1% of the class
2. in the highest 25% of the class
3. in the second-highest 25% of the class
4. in the second-lowest 25% of the class
5. in the lowest 25% of the class
42. Imagine that you conduct an experiment with a penny that is unbiased, so the probability is 50% that it will come up ''heads'' and 50% that it will come up ''tails'' on any given toss. If you toss this coin n times, where n is a natural number and is at least 1, the probability Pn that the coin will come up ''heads'' on every toss is
1. Pn = 1/n
2. Pn = 2n
3. Pn = 1/(2n)
4. Pn = n/2
5. none of the above
43. Suppose you plot the formula derived in the previous question as points on a graph, and then connect the points by curve fitting. Which of the curves in Fig. Exam-5 is the best representation of the result?
1. A
2. B
3. C
4. D
5. None of them.
44. A variable whose value cannot be predicted in any given instance is called
1. a random variable
2. a discrete variable
3. a continuous variable
4. a dependent variable
5. an independent variable
45. Time is often portrayed in graphs as the
1. mode
2. standard deviation
3. variance
4. independent variable
5. line of least squares
46. Inaccuracy can be introduced into an experiment when a person reads an analog instrument such as a conventional ''pointer style'' meter, even if the meter is working perfectly, because of
1. interpolation error
2. a sampling frame that is too small
3. failure to choose a random sample
4. the choice of a biased sample
5. confusion of independent and dependent variables
47. When a hypothesis is made with the intent that it be tested, ultimately (we hope) to be either shown true or else proven not true, that hypothesis is called
1. a propositional hypothesis
2. a sample hypothesis
3. a subjective hypothesis
4. a null hypothesis
5. a median hypothesis
48. Suppose an experiment is conducted to determine how many human-hours are spent watching each of the numerous different satellite television channels in the United States. Suppose the channels are arbitrarily numbered 1, 2, 3, 4, and so on. After the experiment has been completed and the data has been gathered, a graph is plotted in which the number of human-hours in the year 2003 is plotted as a function of the channel number. The channel numbers constitute
1. a continuous variable
2. a discrete variable
3. a dependent variable
4. a horizontal variable
5. a frequency variable
49. Table Exam-3 shows an example of
1. ordered sampling
2. continuous sampling
4. sampling with replacement
5. sampling with correlation
50. Which of the following correlation figures (a), (b), (c), or (d) is implausible?
1. r = +0.5
2. r = +25%
3. r = –75%
4. r = –5
5. All of the above (a), (b), (c), and (d) are plausible.
51. Suppose you want to figure out the quantitative effect that the consumption of fat has on people's cholesterol levels. You ask some people how much fat they eat, and you measure their cholesterol levels. The population for your experiment is the set of all people in the world. You choose a sampling frame that consists of 10 people from each officially recognized country in the world. Which, if any, of the following (a), (b), or (c) points to a potential flaw in this scheme?
1. People cannot in general accurately tell how much fat they eat.
2. The sampling frame is extremely small.
3. Factors other than fat consumption can affect cholesterol levels.
4. None of the above (a), (b), or (c) points to a flaw in the scheme.
5. All of the above (a), (b), and (c) point to flaws in the scheme.
52. Fill in the blank to make the following sentence true: ''If the measurement unit of either variable in a graph is changed in size but still refers to the same phenomenon (for example, miles to kilometers or degrees Celsius to degrees Fahrenheit), the plot may be distorted vertically or horizontally, but the _____, if any, between the two variables is not affected.''
1. standard deviation
2. variance
3. correlation
4. mode
5. median
53. Imagine two sets that have no elements in common. These sets are said to be
1. null-coincident
2. minimally coincident
3. intersecting
4. element-free
5. disjoint
54. Figure Exam-6 illustrates two normal distributions, represented by curves X and Y. Which, if any, of the following statements (a), (b), (c), or (d) is false?
1. The standard deviation of the distribution represented by curve X differs from the standard deviation of the distribution represented by curve Y.
2. The variance of the distribution represented by curve X differs from the variance of the distribution represented by curve Y.
3. The coefficient of variation of the distribution represented by curve X differs from the coefficient of variation of the distribution represented by curve Y.
4. The mean of the distribution represented by curve X differs from the mean of the distribution represented by curve Y.
5. All of the above statements (a), (b), (c), and (d) are true.
55. What is the smallest number of elements a set can have?
1. Less than 0
2. 0
3. 1
4. More than 1
5. Infinitely many
56. What, if anything, is wrong or implausible with Fig. Exam-7?
1. The sampling frame should be, but is not, a subset of the population.
2. The sample should be, but is not, a subset of the sampling frame.
3. The population should be, but is not, a subset of the sampling frame.
4. The sampling frame should be, but is not, a subset of the sample.
5. Nothing is wrong or implausible with Fig. Exam-7.
57. Suppose the correlation between two variables is as weak as it can possibly be. Which of the following expresses the correlation, r, in quantitative form?
1. r = –100
2. r = –1
3. r = –100%
4. r = –1%
5. None of the above.
58. Consider a statistical distribution. Suppose someone tells you, ''The sampling distribution of means gets less and less like a normal distribution as the sample size increases.'' This statement
1. is true only if the mean, median, and mode are all the same
2. is true only for infinite populations
3. is true only for large populations
4. is true only for small populations
5. is patently false
59. The decimal expansion of the square root of 10
1. is a relation but not a function
2. is a function but not a relation
3. cannot be written out in its entirety
4. is an integer
5. is not a real number
60. Imagine a scatter plot in which almost all of the points lie near a straight line, but there are a few points that are far away from the main group. Stray points of this sort are called
1. nonlinear points
2. points of greatest squares
3. points of least squares
4. error points
5. none of the above
61. Figure Exam-8 is an example of
1. a scatter plot
2. a point-to-point graph
3. linear interpolation
4. a least-squares line
62. The dashed curve in Fig. Exam-8 represents
1. a least-squares line
2. a point-to-point graph
3. linear interpolation
4. a regression curve
63. Consider the set of all people in the state of Arizona who smoke cigarettes. Call this set As. Suppose John lives in Arizona and smokes cigarettes. John is
1. a sampling frame with respect to As
2. a subset of As
3. a proper subset of As
4. an element of As
5. a population frame of As
64. One of the major ways in which an error can be made when formulating hypotheses is to assume that the null hypothesis is false, and then
1. have the experiment confirm that it is false
2. have the experiment show that it is true
3. have the experiment show that one alternative hypothesis is true
4. have the experiment show that two of the alternative hypotheses are true
5. have the experiment show that all of the alternative hypotheses are true
65. Pseudorandom numbers
1. can be generated by having a child chatter off digits out loud
2. are theoretically random
3. are equivalent to theoretically random numbers for practical purposes
4. can be generated by spinning a wheel
5. have a correlation of –1
66. Table Exam-4 shows temperature and rainfall data for a hypothetical town. What, if anything, is wrong with this table? If anything is wrong, how can the table be made correct?
1. The data in the left-hand and middle columns is entered incorrectly. The entries in these columns should be transposed.
2. The data in the left-hand and right-hand columns is entered incorrectly. The entries in these columns should be transposed.
3. The data in the middle and right-hand columns is entered incorrectly. The entries in these columns should be transposed.
4. The data in the left-hand column does not add up correctly. The addition errors should be corrected.
5. Nothing is wrong with Table Exam-4.
67. Assuming that Table Exam-4 is correct as shown, or that it is corrected if it contains errors, what can be said about the correlation between the average monthly temperature and the average monthly rainfall for this hypothetical town?
1. There is no correlation.
2. It is negative.
3. It is positive.
4. It is a null hypothesis.
5. Nothing. It is impossible to tell if there is correlation or not.
68. Suppose a computer is programmed to find the correlation between two variables, and the correlation is found to be 0. The computer is then programmed to produce a scatter plot and identify the least-squares line (if there is one) for the points in the plot. The computer will show us that the least-squares line
1. ramps downward as you move toward the right
2. ramps upward as you move toward the right
3. is not straight, but is a parabola
4. is not straight, but is a hyperbola
5. does not exist
69. Suppose a computer is programmed to find the correlation between two variables, and the correlation is found to be 0. The computer is then programmed to produce a scatter plot. The points in the plot will most likely
1. be spread out all over the graph
2. lie along a line or curve that ramps upward as you move toward the right
3. lie along a line or curve that ramps downward as you move toward the right
4. lie along a parabola
5. lie along a hyperbola
70. Imagine that tornadoes occur in a given county on the average of one event every 3 years. Suppose 10 years go by and there are no tornadoes in that county. Then, in the next year, there are 3 tornadoes. This should not surprise us because
1. bunching-up of events simply happens in nature from time to time
2. the law of averages forced it
3. tornadoes were ''due'' in the county
4. nature built up a ''tornado deficit'' in the county that had to be ''paid off''
5. the butterfly effect forced it to happen
71. Two outcomes are mutually exclusive if and only if
1. they always occur in every situation
2. they have some of their elements in common
3. they have all their elements in common
4. they have no elements in common
5. they never occur in any situation
72. When sampling is done with replacement in a finite set:
1. the size of the set does not change
2. the size of the set increases
3. the size of the set decreases
4. the size of the set becomes negative
5. none of the above
73. The butterfly effect is responsible for the fact that
1. variables are always correlated, even when it seems that they are not
2. cause–effect often works in the opposite way from what we would expect
3. localized, small events can have widespread, large-scale consequences
4. things always happen in bunches
5. if there is an upper bound, then there is a least upper bound
74. A sequence of digits from the set {0, 1, 2, 3, 4, 5, 6, 7, 8, 9} can be considered random
1. if and only if they can be written down as a nonterminating, repeating sequence
2. if and only if they coincide with the digits in the decimal expansion of some specific irrational number such as the square root of 2
3. if and only if, given any digit in the sequence, the next one is a function of it
4. if and only if, given any digit in the sequence, there exists no way to predict the next one
5. if and only if they are generated by a calculator or computer
75. Suppose the distance between the dashed line and each of the points in Fig. Exam-9 is measured, producing a set of distance numbers. These numbers are squared and then the squares are added up, getting a final sum D. The dashed line in Fig. Exam-9 represents the line for which D is minimized for the set of points shown. This means that the dashed line is the
1. mean correlation line
2. interpolation line
3. least-squares line
4. median line
5. function line
76. In a uniform distribution, the value of the function is
1. peaked at one point
2. always equal to 0
3. constant
4. increasing
5. decreasing
77. If either scale in a graph of a function has a span that is not large enough, then
1. it doesn't really matter, although it might look bad
2. the dependent and independent variables might be confused with each other
3. there won't be enough room to illustrate the whole function, or the part we're most interested in
4. space in the graph will be wasted
5. the graph will appear cluttered
78. In a scatter plot, the correlation is defined by
1. the nearness of the points to a particular circle
2. the nearness of the points to a particular straight line
3. the nearness of the points to the horizontal axis
4. the nearness of the points to the vertical axis
5. the number of points overall
79. Which of the following situations has probability of 0 in the real world – that is, it never occurs?
1. The mean, median, and mode in a distribution can all be the same.
2. The correlation between two variables can be less than 0.
3. Two events can be caused by a third event.
4. A minuscule event can have huge consequences.
5. None of the above situations has probability 0 in the real world.
6. That is to say, any of them can occur.

80. Suppose you are about to relocate to New York City. You wonder what proportion of the people there eat sushi at least once a week. You assume that the figure is 20%. I think the proportion is higher than that, and I will try to prove you wrong. My contention is an example of
1. a null hypothesis
2. an alternative hypothesis
3. a standard deviation
4. weak correlation
5. strong correlation
81. Quartile points break a data set up into intervals, each interval containing approximately _____ of the elements in the set.
1. 1/2
2. 1/3
3. 1/4
4. 1/10
5. 1/100
82. Which, if any, of the following (a), (b), (c), or (d) is an example of statistical inference?
1. An alternative hypothesis.
2. A null hypothesis.
3. A significance test.
4. A confidence interval.
5. None of the above (a), (b), (c), or (d) is an example of statistical inference.
83. Suppose we want to see how income correlates with age, and we have the financial records of 500 people (which we obtained with their permission). The clearest way to graphically illustrate this correlation, if there is any, is to put the data in the form of
1. a table
2. a scatter plot
3. a null graph
4. a pie graph
5. a bar graph
84. Sampling is a process of
1. analyzing data
2. gathering data
3. determining correlation
4. determining cause-and-effect
5. graphing functions
85. What is the real-number solution set for x2 –7x + 12 = 0?
1. {–7, 12}
2. {7, –12}
3. {3, 4}
4. {–3, –4}
5. There are no real-number solutions to this equation.
86. Refer to Fig. Exam-10. The curve is ''bell-shaped'' and is symmetrical on the left-hand and right-hand sides of the heavy, vertical dashed line labeled x = μ. This is a classical illustration of
1. a uniform distribution
2. a bimodal distribution
3. a discrete distribution
4. a normal distribution
5. a discontinuous distribution
87. In Fig. Exam-10, the symbol μ is meant to represent
1. the mean
2. the median
3. the mode
4. the variance
5. the standard deviation
88. In Fig. Exam-10, the symbol σ is meant to represent
1. the mean
2. the median
3. the mode
4. the variance
5. the standard deviation
89. Figure Exam-11 is an example of
1. a scatter plot
2. a correlation graph
3. linear interpolation
4. curve fitting
5. a bar graph
90. The numbers to the right of the shaded rectangles in Fig. Exam-11 are there
1. to clarify the values represented by the rectangles
2. to make the graph appear less cluttered
3. to make the graph look more sophisticated
4. to provide data for making other graphs
5. for no useful reason
91. Figure Exam-12 shows the results of a 100-question test given to a large group of students. The boundary points in this nomograph define the
1. quartiles
2. deciles
3. percentiles
4. equal intervals
5. none of the above
92. What, if anything, is wrong or implausible with the nomograph in Fig. Exam-12?
1. The boundary points should be equally spaced.
2. There should be 10 points, not 9.
3. There should be points representing scores of 0 and 100.
4. There should be a point representing a score of 50.
5. Nothing is wrong or implausible with the nomograph in Fig. Exam-12.
93. If no data are available, statisticians must collect it themselves. Data collected directly by the statisticians who analyze it is known as
1. independent source data
2. dependent source data
3. primary source data
4. secondary source data
5. none of the above
94. As the size of an experimental sample set increases:
1. the size of the population increases
2. the size of the population decreases
3. the estimate of the mean can be done with less and less accuracy
4. the estimate of the mean can be done with more and more accuracy
5. the standard deviation approaches 0
95. Which of the following statements (a), (b), (c), or (d) is true?
1. The values in a bar graph do not necessarily have to add up to 100%.
2. Some functions are relations.
3. Zero correlation is indicated by widely scattered points on a graph.
4. A histogram is a specialized bar graph.
5. All of the above statements (a), (b), (c), and (d) are true.
96. Suppose it's autumn in Minnesota, and you predict that it will be an average winter temperature-wise, based on historical data. This is a null hypothesis. Your uncle Jim thinks it will be a colder winter than average. Your sister Susan thinks it will be either warmer or colder than average, but not average. Uncle Jim's prediction is an example of
1. a one-sided alternative hypothesis
2. a two-sided alternative hypothesis
3. a positive hypothesis
4. a negative hypothesis
5. an off-center hypothesis
97. Suppose it's autumn in Minnesota, and you predict that it will be an average winter temperature-wise, based on historical data. This is a null hypothesis. Your uncle Jim thinks it will be a colder winter than average. Your sister Susan thinks it will be either warmer or colder than average, but not average. Susan's prediction is an example of
1. a one-sided alternative hypothesis
2. a two-sided alternative hypothesis
3. a positive hypothesis
4. a negative hypothesis
5. an off-center hypothesis
98. Consider the following process for limiting the length of a number to three decimal places:
99. The steps in this process are examples of

1. rounding
2. variance
3. normalization
4. truncation
5. standard deviation
100. As the number of events in an experiment increases, the average value of the outcome approaches the theoretical mean. This is a statement of
1. the law of least squares
2. the Central Limit Theorem
3. the law of large numbers
4. the Regression Theorem
5. the butterfly effect
101. In the plot of Fig. Exam-13, the correlation between phenomenon X and phenomenon Y appears to be
1. positive
2. negative
3. zero
4. linear
5. undefined
102. With respect to the plot shown by Fig. Exam-13, which of the following scenarios (a), (b), (c), or (d) is plausible?
1. Changes in the frequency, intensity, or amount of X cause changes in the frequency, intensity, or amount of Y.
2. Changes in the frequency, intensity, or amount of Y cause changes in the frequency, intensity, or amount of X.
3. Changes in the frequency, intensity, or amount of some third factor, Z, cause changes in the frequencies, intensities, and amounts of both X and Y.
4. There is no cause–effect relationship between X and Y whatsoever.
5. Any of the above scenarios (a), (b), (c), or (d) is plausible.
103. Two outcomes are independent if and only if
1. they both lie along the least-squares line in a scatter plot
2. they are perfectly correlated
3. the occurrence of one outcome affects the probability that the other will occur
4. the occurrence of one outcome does not affect the probability that the other will occur
5. Wait! The premise is implausible. Two outcomes in an experiment can never be independent.

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