Statistics Chapter 1: Key Concepts and Sample Questions

Chapter 1 Introduction 1. A portion of the population selected to represent the population is called _____. a. statistical inference b. descriptive statistics c. a census d. a sample 2. A sample of five Fortune 500 companies possessed the following industry codes: banking, banking, finance, retail, and banking. Based on this information, which of the following statements is correct? a. Sixty percent of the sample of five companies are banking industries. b. Sixty percent of all Fortune 500 companies are banking industries. c. Banking is the most common type of industry among all Fortune 500 companies. d. If five other Fortune 500 companies were chosen, 60% of them would be banking industries. 3. Categorical data _____. a. are always nonnumeric b. may be either numeric or nonnumeric c. are always numeric d. indicate either how much or how many 4. Categorical data use either the ______ or ______ scale of measurement. a. nominal; ordinal b. nominal; interval c. ordinal; interval d. interval; ratio 5. Flight time from Cincinnati to Atlanta is an example of a _____ variable and _____ measurement. a. discrete; interval b. discrete; ratio c. continuous; interval d. continuous; ratio 6. For ease of data entry into a university database, 1 denotes the student is enrolled in an undergraduate degree program, 2 indicates the student is enrolled in a master’s degree program, and 3 indicates the student is enrolled in a doctoral degree program. In this case, the data are which scale of measurement? a. nominal

b. ordinal c. interval d. ratio 7. In a post office, the mailboxes are numbered from 1 to 5,000. These numbers represent _____. a. categorical data b. time series data c. cross-sectional data d. quantitative data 8. In an application for a credit card, potential customers are asked for their social security numbers. A social security number is an example of a _____. a. categorical variable b. quantitative variable c. categorical or quantitative variable, depending on how the respondents answered the question d. ratio variable 9. Quantitative data _____. a. are always nonnumeric b. may be either numeric or nonnumeric c. are always numeric d. are always labels 10. Quantitative data that measure "how many" are ________; quantitative data that measure "how much" are ________. a. interval; ratio b. ratio; interval c. continuous; discrete d. discrete; continuous 11. Temperature is an example of which scale of measurement? a. nominal b. ordinal c. interval d. ratio 12. The Department of Transportation of a city has noted that on the average there are 14 accidents per day. The average number of accidents is an example of _____. a. descriptive statistics b. statistical inference

c. a sample d. a population 13. The owner of a factory regularly requests a graphical summary of all employees' salaries. The graphical summary of salaries is an example of _____. a. a sample b. descriptive statistics c. statistical inference d. an experiment 14. The process of analyzing sample data to draw conclusions about the characteristics of a population is called _____. a. descriptive statistics b. statistical inference c. data analysis d. data summarization 15. When the data are labels or names used to identify an attribute of the elements, the variable has which scale of measurement? a. nominal b. ordinal c. interval d. ratio 16. When the data are labels or names used to identify an attribute of the elements and the rank of the data is meaningful, the variable has which scale of measurement? a. nominal b. ordinal c. interval d. ratio 17. When the data have the properties of interval data and the multiplication or division of two values is meaningful, the variable has which scale of measurement? a. nominal b. ordinal c. interval d. ratio

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18. When the data have the properties of ordinal data and the interval between observations is expressed in terms of a fixed unit of measure, the variable has which scale of measurement? a. nominal b. ordinal c. interval d. ratio 19. Which of the following is NOT a scale of measurement? a. nominal b. ordinal c. interval d. categorical 20. Which of the following is NOT an example of descriptive statistics? a. a histogram depicting the age distribution for 30 randomly selected students b. an estimate of the number of Alaska residents who have visited Canada c. a table summarizing the data collected in a sample of new-car buyers d. the proportion of mailed-out questionnaires that were returned 21. Which of the following is an example of quantitative data? a. the player’s number on a baseball uniform b. the serial number on a one-dollar bill c. the part number of an inventory item d. the number of people in a waiting line 22. Which of the following variables uses the interval scale of measurement? a. name of stock exchange b. time c. SAT scores d. social security number 23. Which of the following variables uses the ratio scale of measurement? a. name of stock exchange b. time c. SAT scores d. social security number 24. Which two scales of measurement can be either numeric or nonnumeric?

a. nominal and ratio b. ordinal and interval c. interval and ordinal d. nominal and ordinal Chapter 2 Data Summary: Tabular Presentation and Charts 1. A _____ shows the proportion of data items. a. histogram b. cumulative percent frequency distribution c. stem-and-leaf display d. cumulative relative frequency distribution 2. A _____can be used to graphically present quantitative data. a. bar chart b. pie chart c. stem-and-leaf display d. stacked bar chart 3. A frequency distribution is a _____. a. tabular summary of a set of data showing the fraction of items in each of several nonoverlapping classes b. graphical form of representing data c. tabular summary of a set of data showing the number of items in each of several nonoverlapping classes d. graphical device for presenting categorical data 4. A graphical device for presenting categorical data summaries based on subdivision of a circle into sectors that correspond to the relative frequency for each class is a _____. a. histogram b. stem-and-leaf display c. pie chart d. bar chart 5. A graphical method that can be used to show both the rank order and shape of a data set simultaneously is a _____. a. relative frequency distribution b. pie chart c. stem-and-leaf display

d. pivot table 6. A graphical presentation of a frequency distribution, relative frequency distribution, or percent frequency distribution of quantitative data constructed by placing the class intervals on the horizontal axis and the frequencies on the vertical axis is a _____. a. histogram b. bar chart c. stem-and-leaf display d. pie chart 7. A histogram is NOT appropriate for displaying which of the following types of information? a. frequency b. relative frequency c. cumulative frequency d. percent frequency 8. Categorical data can be graphically represented by using a(n) _____. a. histogram b. stem-and-leaf display c. scatter diagram d. bar chart 9. For stem-and-leaf displays where the leaf unit is not stated, the leaf unit is assumed to equal _____. a. 0 b. 0.1 c. 1 d. 10 10. Frequency distributions can be made for _____. a. categorical data only b. quantitative data only c. neither categorical nor quantitative data d. both categorical and quantitative data 11. In a stem-and-leaf display, _____. a. a single digit is used to define each stem, and a single digit is used to define each leaf b. a single digit is used to define each stem, and one or more digits are used to define each leaf c. one or more digits are used to define each stem, and a single digit is used to define each leaf d. one or more digits are used to define each stem, and one or more digits are used to define each leaf

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12. In constructing a frequency distribution, as the number of classes is decreased, the class width _____. a. decreases b. remains unchanged c. increases d. can increase or decrease depending on the data values 13. The height and weight are recorded by the school nurse for every student in a school. What type of graph would best display the relationship between height and weight? a. bar graph b. stem-and-leaf plot c. histogram d. scatter diagram 14. There are 20 boys and 8 girls in a class. What type of graph can be used to display this information? a. bar graph b. stem-and-leaf plot c. histogram d. scatter diagram 15. What is the difference between a bar graph and a histogram? a. There is no difference between a bar graph and a histogram. b. A bar graph displays categorical data, while a histogram displays quantitative data. c. A bar graph has no spaces between the bars, while a histogram must have space between the bars. d. A bar graph displays quantitative data, while a histogram displays categorical data. Chapter 3 Descriptive Statistics 1. A graph with skewness –1.8 would be which of the following? a. moderately skewed left b. highly skewed left c. moderately skewed right d. highly skewed right 2. A graphical summary of data that is based on a five-number summary is a _____. a. histogram

b. stem-and-leaf display c. scatter diagram d. boxplot 3. A numerical measure of linear association between two variables is the _____. a. variance b. covariance c. standard deviation d. coefficient of variation 4. After the data have been arranged from smallest value to largest value, the value in the middle is called the _____. a. range b. median c. mean d. interquartile range 5. An important measure of location for categorical data is the _____. a. mean b. median c. mode d. range 6. During a cold winter, the temperature stayed below zero for 10 days (ranging from –20 to –5). The variance of the temperatures of the 10 day period _____. a.is negative since all the numbers are negative b. must be at least zero c. cannot be computed since all the numbers are negative d. can be either negative or positive 7. For data skewed to the left, the skewness is _____. a. between 0 and .5 b. less than 1 c. positive d. negative 8. Generally, which of the following is the least appropriate measure of central tendency for a data set that contains outliers? a. mean

b. median c. mode d. midrange 9. If a data set has an even number of observations, the median _____. a. cannot be determined b. is the observation recorded most often c. must be equal to the mean d. is the average value of the two middle items when all items are arranged in ascending order 10. If r = 0.48 for data set A and r = –0.48 for data set B, which of the following is true? a. The variables in A are more strongly correlated than the variables in B. b. The data values in A are all positive, while the data values in B are all negative. c. The two data sets have the same level of correlation. d. The two data sets have an almost perfect linear relationship between their respective variables. 11. If the data distribution is symmetric, the skewness is _____. a. 0 b. .5 c. 1 d. –.5 12. If the variance of a data set is correctly computed with the formula using n − 1 in the denominator, which of the following is true? a. The data set is a sample. b. The data set is a population. c. The data set could be either a sample or a population. d. The data set is from a census. 13. In a five-number summary, which of the following is NOT used for data summarization? a. smallest value b. largest value c. median d. mean 14. Positive values of covariance indicate _____. a. a positive variance of the x values

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b. a positive variance of the y values c. the standard deviation is positive d. a positive relation between the x and y variables 15. The 75th percentile is also the _____. a. first quartile b. second quartile c. third quartile d. fourth quartile 16. The _____ denotes the number of standard deviations xi is from the mean . a. variance b. median c. z-score d. normal deviation 17. The coefficient of variation indicates how large the standard deviation is relative to the _____. a. mean b. median c. range d. variance 18. The correlation coefficient ranges from which two values? a. 0 and 1 b. −1 and +1 c. minus infinity and plus infinity d. 1 and 100 19. The descriptive measure NOT measured in the same units as the original data is the _____. a. median b. standard deviation c. mode d. variance 20. The descriptive measure of dispersion that is based on the concept of a deviation about the mean is the _____. a. range b. interquartile range c. weighted mean

d. standard deviation 21. The difference between the largest and smallest data values is the _____. a. variance b. interquartile range c. range d. coefficient of variation 22. The empirical rule states that, for data having a bell-shaped distribution, the portion of data values being within one standard deviation of the mean is approximately _____. a. 33% b. 50% c. 68% d. 95% 23. The interquartile range is the difference between the _____. a. first and second quartiles b. first and third quartiles c. second and third quartiles d. second and fourth quartiles 24. The interquartile range is used as a measure of variability to overcome what difficulty of the range? a. The sum of the range variances is zero. b. The range is difficult to compute. c. The range is influenced too much by extreme values. d. The range is negative. 25. The mean of the sample _____. a. is always larger than the mean of the population from which the sample was taken b. is always smaller than the mean of the population from which the sample was taken c. c. can never be zero d . is affected by outliers 26. The measure of location often used in analyzing growth rates in financial data is the _____. a. arithmetic mean b. weighted mean c. geometric mean

d. hyperbolic mean 27. The median of a sample will always equal the _____. a. mode b. mean c. 50th percentile d. 75th percentile 28. The standard deviation of a sample of 100 observations is 64. The variance of the sample is which of the following? a. 8 b. 10 c. 6,400 d. 4,096 29. When dividing a data set into four parts, the division points are referred to as the _____. a. class lower limits b. quartiles c. midpoints d. percentiles 30. When the data are positively skewed, the mean will usually be _____. a. less than the median b. greater than the median c. less than the mode d. greater than the mode 31. Which of the following is NOT a measure of location? a. mean b. median c. variance d. mode 32. Which of the following values of r indicates the strongest correlation? a. .82 b. .361 c. 0 d. –.9

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Chapter 4 Probability 1. A couple has three children. Assuming each child has an equal chance of being a boy or a girl, what is the probability that they have at least one girl? a. .125 b. .5 c. .875 d. 1 2. A lottery is conducted using three urns. Each urn contains chips numbered from 0 to 9. One chip is selected at random from each urn. The total number of sample points in the sample space is _____. a. 30 b. 100 c. 729 d. 1,000 3. A professor rolls a fair, six-sided die. Using the classical method of probability, what is the probability that at least three spots will be showing up on the die? a. .5 b. .67 c. .3 d. .167 4. A(n) __________ is a collection of sample points. a. probability b. permutation c. experiment d. event 5. An experiment consists of four outcomes with P(E1) = .2, P(E2) = .3, and P(E3) = .4. The probability of outcome E4 is _____. a. .500 b. .024 c. .100 d. .900

6. An experiment consists of three steps. There are four possible results on the first step, three possible results on the second step, and two possible results on the third step. The total number of experimental outcomes is _____. a. 9 b. 14 c. 24 d. 36 7. Bayes' theorem is used to compute _____. a. the prior probabilities b. the union of events c. the intersection of events d. the posterior probabilities 8. Events A and B are mutually exclusive with P(A) = .3 and P(B) = .2. The probability of the complement of event B equals _____. a. 0 b. .06 c. .70 d. .80 9. If A and B are independent events with P(A) = .05 and P(B) = .65, then P(A | B) = _____. a. .05 b. .0325 c. .65 d. .8 10. If A and B are independent events with P(A) = 0.1 and P(B) = .4, then _____. a. P(A ∩ B) = 0 b. P(A ∩ B) = .04 c. P(A ∩ B) = .5 d. P(A ∩ B) = .25 11. If A and B are independent events with P(A) = .2 and P(B) = .6, then P(A B) = _____. a. . 62 b. . 12 c.

.6 0 d. . 68 12. If A and B are independent events with P(A) = .4 and P(B) = .6, then P(A ∩ B) = _____. a. .76 b. 1 c. .24 d. .2 13. If A and B are mutually exclusive events with P(A) = .3 and P(B) = 0.5, then P(A ∩ B) = a. .30 b. .15 c. 0 d. .20 14. If A and B are mutually exclusive events with P(A) = .3 and P(B) = .5, then P(A B) = a. 0 b. .15 c. .8 d. .2 15. If P(A | B) = .3 and P(B) = .8, then _____. a. P(A) = .24 b. P(B | A) = .7 c. P(A ∩ B) = .5 d. P(A ∩ B) = .24 16. If P(A ∩ B) = 0, _____. a. P(A) + P(B) = 1 b. either P(A) = 0 or P(B) = 0 c. A and B are mutually exclusive events d. A and B are independent events 17. If P(A) = .50, P(B) = .60, and P(A ∩ B) = .30, then events A and B are _____. a. mutually exclusive events

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b. dependent events c. independent events d. posterior probabilities 18. If P(A) = .6, P(B) = .3, and P(A ∩ B) = .2, then P(B | A) =_____. a. .33 b. .5 c. .67 d. .9 19. If P(A) = .62, P(B) = .56, and P(A B) = .70, then P(B | A) = _____. a. .4800 b. .7742 c. .9032 d. .6340 20. If P(A) = .75, P(A B) = .86, and P(A ∩ B) = .56, then P(B) = a. .25 b. .67 c. .56 d. .11 21. If X and Y are mutually exclusive events with P(X) = .295, P(Y) = .32, then P(X ∩ Y) = _____. a. .094 b. .615 c. 1 d. 0 22. If a coin is tossed three times, the likelihood of obtaining three heads in a row is _____. a. 0 b. .500 c. .875 d. .125 23. If a fair penny is tossed four times and comes up heads all four times, the probability of heads on the fifth trial is _____. a. 0

b. .03125 c. .50 d. .20 24. If two events are independent, then _____. a. they must be mutually exclusive b. the sum of their probabilities must be equal to 1 c. the probability of their intersection must be 0 d. the events have no influence on each other 25. In an experiment, events A and B are mutually exclusive. If P(A) = .6, then the probability of B _____. a. cannot be larger than .4 b. can be any value greater than .6 c. can be any value between 0 and 1 d. must also be .6 26. Of five letters (A, B, C, D, and E), two letters are to be selected at random. How many possible selections are there? a. 20 b. 7 c. 5 d. 10 27. The "Top Three" at a racetrack consists of picking the correct order of the first three horses in a race. If there are 10 horses in a particular race, how many "Top Three" outcomes are there? a. 302,400 b. 720 c. 1,814,400 d. 10 28. The complement of P(A | B) is _____. a. P(A c | B) b. P(A | B c ) c. P(B | A) d. P(A I B) 29. The probability of at least one head in two flips of a coin is _____.

a. .33 b. .50 c. .75 d. 1 30. Two events are mutually exclusive if _____. a. the probability of their intersection is 1 b. they have no sample points in common c. the probability of their intersection is .5 d. the probability of their intersection is 1 and they have no sample points in common 31. Two events with nonzero probabilities _____. a. can be both mutually exclusive and independent b. cannot be both mutually exclusive and independent c. are always mutually exclusive d. are always independent

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