Practice Questions Chapter 1 and 2

Practice Questions Chapter 1 and 2

Multiple Choice

Identify the choice that best completes the statement or answers the question.

1. Which of the following is not an example of descriptive statistics? a. a histogram depicting the age distribution for 30 randomly selected studentsb. an estimate of the number of Alaska residents who have visited Canadac. a table summarizing the data collected in a sample of new-car buyersd. the proportion of mailed-out questionnaires that were returned

2. A characteristic of interest for the elements is called a(n) a. sampleb. data setc. variabled. observation

3. In a data set, the number of observations will always be the same as the number of a. variablesb. elementsc. data setsd. data

4. Categorical data a. are always nonnumericb. may be either numeric or nonnumericc. are always numericd. indicate either how much or how many

5. 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 variableb. quantitative variablec. categorical or quantitative variable, depending on how the respondents answered the questiond. ratio variable

6. Temperature is an example of a. a categorical variableb. a quantitative variablec. either a quantitative or categorical variabled. neither a quantitative nor categorical variable

7. Statistical studies in which researchers do not control variables of interest are a. experimental studiesb. uncontrolled experimental studiesc. not of any valued. observational studies

8. Statistical studies in which researchers control variables of interest are a. experimental studiesb. control observational studiesc. non experimental studiesd. observational studies

9. 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 ofa. descriptive statisticsb. statistical inferencec. a sampled. a population

10. The process of analyzing sample data in order to draw conclusions about the characteristics of a population is calleda. descriptive statisticsb. statistical inferencec. data analysisd. data summarization

11. In a post office, the mailboxes are numbered from 1 to 5,000. These numbers representa. categorical datab. time series datac. either categorical or quantitative datad. quantitative data

12. Since a sample is a subset of the population, the sample meana. is always smaller than the mean of the populationb. is always larger than the mean of the populationc. must be equal to the mean of the populationd. can be larger, smaller, or equal to the mean of the population

13. 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 leafb. a single digit is used to define each stem, and one or more digits are used to define each leafc. one or more digits are used to define each stem, and a single digit is used to define each leafd. one or more digits are used to define each stem, and one or more digits are used to define each leaf

14. A frequency distribution isa. a tabular summary of a set of data showing the fraction of items in each of several nonoverlapping classesb. a graphical form of representing datac. a tabular summary of a set of data showing the number of items in each of several nonoverlapping classesd. a graphical device for presenting categorical data

15. In a cumulative frequency distribution, the last class will always have a cumulative frequency equal toa. oneb. 100%c. the total number of elements in the data setd. None of the other answers are correct.

Exhibit 2-3

The number of sick days taken (per month) by 200 factory workers is summarized below.Number of Days | Frequency1 − 5 | 1206 − 10 | 6511 − 15 | 1416 − 20 | 1

16. Refer to Exhibit 2-3. The class width for this distribution a. is 6b. is 5c. is 20, which is: the largest value minus the smallest value or 20 − 0 = 20d. varies from class to class

17. Refer to Exhibit 2-3. The number of workers who took at most 10 sick days per month a. was 15b. was 200c. was 185d. was 65

18. Qualitative data can be graphically represented by using a(n) a. histogramb. frequency polygonc. ogived. bar graph

19. Fifteen percent of the students in a School of Business Administration are majoring in Economics, 20% in Finance, 35% in Management, and 30% in Accounting. The graphical device(s) that can be used to present these data is (are)a. a line graphb. only a bar graphc. only a pie chartd. both a bar graph and a pie chart

20. The total number of data items with a value less than or equal to the upper limit for the class is given by thea. frequency distributionb. relative frequency distributionc. cumulative frequency distributiond. cumulative relative frequency distribution

21. A common graphical presentation of quantitative data is aa. histogramb. bar graphc. relative frequencyd. pie chart

22. A tabular method that can be used to summarize the data on two variables simultaneously is calleda. simultaneous equationsb. a crosstabulationc. a histogramd. a dot plot

23. When the conclusions based upon the aggregated crosstabulation can be completely reversed if we look at the unaggregated data, the occurrence is known asa. reverse correlationb. inferential statisticsc. Simpson's paradoxd. disaggregation

24. The interquartile range is the difference between thea. first and second quartilesb. first and third quartilesc. second and third quartilesd. second and fourth quartiles

25. After the data has been arranged from smallest value to largest value, the value in the middle is called thea. rangeb. medianc. meand. None of the other answers are correct.

26. If a data set has an even number of observations, the median a. can not be determinedb. is the average value of the two middle itemsc. must be equal to the meand. is the average value of the two middle items when all items are arranged in ascending order

27. In computing the p th percentile, if the index i is an integer the pth percentile is thea. data value in position ib. data value in position i + 1c. average of data values in position i and i + 1

28. The first quartilea. contains at least one third of the data elementsb. is the same as the 25th percentilec. is the same as the 50th percentiled. is the same as the 75th percentile

29. The measure of location that is the most likely to be influenced by extreme values in the data set is thea. rangeb. medianc. moded. mean

30. The variance of the sample a. can never be negativeb. can be negativec. cannot be zerod. cannot be less than one

31. The value of the sum of the squared deviations from the mean, i.e., must always bea. less than the meanb. negativec. either positive or negative depending on whether the mean is negative or positived. at least zero

32. The coefficient of variation is a. the same as the varianceb. the square root of the variancec. the square of the standard deviationd. None of the other answers are correct.

33. Which of the following symbols represents the mean of the population? a. σ 2b. σc. μd.

34. Which of the following symbols represents the variance of the population? a. σ 2b. σc. μd.

35. The symbol σ 2 is used to represent thea. variance of the populationb. standard deviation of the samplec. standard deviation of the populationd. None of the other answers are correct.

36. Which of the following symbols represents the standard deviation of the population? a. σ 2b. σc. μd.

37. can be used to make statements about the proportion of data values that must be within a specified number of standard deviations of the mean. a. Chebyshev's theoremb. empirical rulec. five-number summaryd. box plot

38. In a five-number summary, which of the following is not used for data summarization? a. the smallest valueb. the largest valuec. the mediand. the mean

39. A numerical measure of linear association between two variables is the a. varianceb. covariancec. standard deviationd. coefficient of variation

40. An important numerical measure of the shape of a distribution is the a. correlation coefficientb. variancec. skewnessd. relative location

Answer Section

1. ANS: B

2. ANS: C

3. ANS: B

4. ANS: B

5. ANS: A

6. ANS: B

7. ANS: D

8. ANS: A

9. ANS: A

10. ANS: B

11. ANS: A

12. ANS: D

13. ANS: C

14. ANS: C

15. ANS: C

16. ANS: B

17. ANS: C

18. ANS: D

19. ANS: D

20. ANS: C

21. ANS: A

22. ANS: B

23. ANS: C

24. ANS: B

25. ANS: B

26. ANS: D

27. ANS: C

28. ANS: B

29. ANS: D

30. ANS: A

31. ANS: D

32. ANS: D

33. ANS: C

34. ANS: A

35. ANS: A

36. ANS: B

37. ANS: A

38. ANS: D

39. ANS: B

40. ANS: C

1. In an experiment involving 80 telephone calls aimed at selling a specific insurance policy, the random variable is the number of sales made. This random variable is categorized as:

   • a. discrete random variable

   • b. continuous random variable

   • c. complex random variable

   • d. None of the answers is correct.

2. The weight of an object, measured in grams, serves as an example of:

   • a. a continuous random variable

   • b. a discrete random variable

   • c. either a continuous or a discrete random variable, depending on the weight of the object

   • d. either a continuous or a discrete random variable depending on the units of measurement

3. The definition of the standard deviation is:

   • a. variance squared

   • b. the square root of the sum of the deviations from the mean

   • c. the same as the expected value

   • d. positive square root of the variance

Exhibit 5-2

The following probability distribution illustrates daily sales at Michael's Co.:

• Daily Sales ($1,000s): Probability40: 0.150: 0.460: 0.370: 0.2

4. From Exhibit 5-2, the expected daily sales amount is:

   • a. $55,000

   • b. $56,000

   • c. $50,000

   • d. $70,000

Exhibit 5-3

The probability distribution detailing the number of goals scored by the Lions soccer team per game is below:

• Number of Goals: Probability0: 0.051: 0.152: 0.353: 0.304: 0.15

5. Based on Exhibit 5-3, the likelihood of the Lions scoring no goals in a game is:

   • a. 0.95

   • b. 0.85

   • c. 0.75

   • d. None of the answers is correct.

Exhibit 5-5

AMR, a computer consulting firm, has the following probability distribution for new clients obtained each month:

• Number of
  New Clients Probability
  0 0.05
  1 0.10
  2 0.15
  3 0.35
  4 0.20
  5 0.10
  6 0.05

  Number of New Clients: Probability0: 0.051: 0.102: 0.153: 0.354: 0.205: 0.106: 0.05

6. In relation to Exhibit 5-5, the variance is:

   • a. 1.431

   • b. 2.0475

   • c. 3.05

   • d. 21

7. Among the characteristics of a binomial experiment, which of the following is true?

   • a. At least two outcomes are possible

   • b. The probability of success varies from trial to trial

   • c. The trials are independent

   • d. All of these answers are correct.

8. The variance for the binomial probability distribution can be expressed as:

   • a. Var(x) = p(1 − p)

   • b. Var(x) = np

   • c. Var(x) = n(1 − p)

   • d. Var(x) = np(1 − p)

9. The standard deviation within a binomial distribution corresponds to:

   • a. E(x) = pn(1 − n)

   • b. E(x) = np(1 − p)

   • c. E(x) = np

   • d. None of the alternative answers is correct.

10. In a binomial experiment characterized by p = 0.5 and a sample size of 100, the expected value is:

• a. 0.50

• b. 0.30

• c. 50

• d. Insufficient information for an answer.

11. Among a class of 100 students, 20% plan to attend graduate school. The corresponding standard deviation for this binomial distribution is:

• a. 20

• b. 16

• c. 4

• d. 2

Exhibit 5-8

In a large university where 60% of the students are female, a random sample of 8 students is chosen.

12. Pertaining to Exhibit 5-8, the variable being examined in this experiment is:

• a. the 60% of female students

• b. the random sample of 8 students

• c. the number of female students from the sample of 8

• d. the size of the student body

Exhibit 5-10

The probability that Pete will catch fish during a fishing expedition is 0.8, and he plans to fish for 3 days next week.

13. According to Exhibit 5-10, the anticipated number of days Pete will successfully catch fish is:

• a. 0.6

• b. 0.8

• c. 2.4

• d. 3

Additional Questions

14. The binomial probability distribution achieves maximum symmetry when:

• a. n is 30 or greater

• b. n equals p

• c. p approaches 1

• d. p equals 0.5

15. For any continuous random variable, the probability of it taking on a specific value is:

• a. 1.00

• b. 0.50

• c. any value between 0 to 1

• d. zero

16. The peak of a normal curve occurs at:

• a. one standard deviation right of the mean

• b. two standard deviations right of the mean

• c. approximately three standard deviations right of the mean

• d. the mean

17. The standard deviation for a standard normal distribution:

• a. is always zero

• b. is always one

• c. can be any positive value

• d. can be any value

18. If Z is a standard normal random variable, then P(-1.5 ≤ z ≤ 1.09) equals:

• a. 0.4322

• b. 0.3621

• c. 0.7953

• d. 0.0711

19. For a standard normal random variable z, what is its value if the area to the right is 0.1112?

• a. 0.3888

• b. 1.22

• c. 2.22

• d. 3.22

20. In a standard normal random variable z, what is its value where the area to the right equals 0.1401?

• a. 1.08

• b. 0.1401

• c. 2.16

• d. -1.08

21. For a standard normal distribution, the probability of obtaining a z value less than 1.6 is:

• a. 0.1600

• b. 0.0160

• c. 0.0016

• d. 0.9452

Exhibit 6-5

The weight of items produced by a machine is normally distributed with a mean of 8 ounces and a standard deviation of 2 ounces.

22. According to Exhibit 6-5, the random variable in this case refers to:

• a. the weight of items produced by the machine

• b. 8 ounces

• c. 2 ounces

• d. the normal distribution

23. In relation to Exhibit 6-5, what percentage of the items will weigh between 6.4 and 8.9 ounces?

• a. 0.1145

• b. 0.2881

• c. 0.1736

• d. 0.4617

Exhibit 6-6

The life expectancy of a specific tire brand is normally distributed, with a mean of 40,000 miles and a standard deviation of 5,000 miles.

24. Referring to Exhibit 6-6, the variable being assessed in this experiment is:

• a. the life expectancy of this tire brand

• b. the normal distribution

• c. 40,000 miles

• d. None of the alternative answers is correct.

25. From Exhibit 6-6, what is the probability that a randomly selected tire will last exactly 47,500 miles?

• a. 0.4332

• b. 0.9332

• c. 0.0668

• d. zero

26. The term for standard deviation in relation to proportion is:

• a. standard proportion

• b. sample proportion

• c. average proportion

• d. standard error of the proportion

27. The standard deviation in relation to the mean is termed:

• a. standard x

• b. standard error of the mean

• c. sample standard mean

• d. sample mean deviation

28. A simple random sample of size n from a finite population of size N must be selected so that each possible sample of size:

• a. N has equal selection probability

• b. n has a 0.5 probability

• c. n has a 0.1 probability

• d. n has the same probability of being selected

29. If a population contains 500 elements, the probability of selecting an element in a simple random sample of 50 on the first draw is:

• a. 0.100

• b. 0.010

• c. 0.001

• d. 0.002

30. A simple random sample of size n drawn from a finite population of size N must have:

• a. same probability of being selected

• b. a probability of 1/n of being selected

• c. a probability of 1/N of being selected

• d. a probability of N/n of being selected

31. A simple random sample from a process (infinite population) is selected under the condition that:

• a. each element belongs to the same population

• b. each element is drawn independently

• c. each element comes from the same population and is drawn independently

• d. probabilities for selection can vary

32. Among the following, which represents a point estimator(s)?

• a. σ

• b. μ

• c. s

• d. All of these answers are correct.

Exhibit 7-2

In a survey of 400 registered voters regarding potential changes to gun laws, 300 said "yes," and 100 said "no."

33. According to Exhibit 7-2, the point estimate of the proportion in the population responding "yes" is:

• a. 300

• b. approximately 300

• c. 0.75

• d. 0.25

Exhibit 7-3

Data gathered from a simple random sample includes the following numbers: 16, 19, 18, 17, 20, 18.

34. Referring to Exhibit 7-3, the point estimate of the population mean is:

• a. 18.0

• b. 19.6

• c. 108

• d. sixteen, since 16 is the smallest value in the sample

35. The expected value for the random variable is:

• a. σ

• b. the standard error

• c. the sample size

• d. μ

36. Within a population of 500 elements, a sample of 225 is drawn. Knowing that the population's variance is 900, the standard error of the mean is approximately:

• a. 1.1022

• b. 2

• c. 30

• d. 1.4847

37. Doubling the sample size will:

• a. reduce the standard error of the mean to half its current value

• b. reduce the standard error of the mean to about 70% of its current value

• c. have no impact on the standard error of the mean

• d. double the standard error of the mean

38. With a population mean of 84 and standard deviation of 12, the probability that the sample mean falls between 80.54 and 88.9 with a sample size of 36 is:

• a. 0.0347

• b. 0.7200

• c. 0.9511

• d. None of the alternative answers is correct.

Exhibit 7-4

A simple random sample of 121 cologne bottles showed an average content of 4 ounces, with a known population standard deviation of 0.22 ounces.

39. According to Exhibit 7-4, the standard error of the mean is:

• a. 0.3636

• b. 0.0331

• c. 0.0200

• d. 4.000

1. In an experiment involving 80 telephone calls aimed at selling a specific insurance policy, the random variable is the number of sales made. This random variable is categorized as: a. discrete random variable b. continuous random variable c. complex random variable d. None of the answers is correct.

2. The weight of an object, measured in grams, serves as an example of: a. a continuous random variable b. a discrete random variable c. either a continuous or a discrete random variable, depending on the weight of the object d. either a continuous or a discrete random variable depending on the units of measurement

3. The definition of the standard deviation is: a. variance squared b. the square root of the sum of the deviations from the mean c. the same as the expected value d. positive square root of the variance

4. From Exhibit 5-2, the expected daily sales amount is: a. $55,000 b. $56,000 c. $50,000 d. $70,000

5. Based on Exhibit 5-3, the likelihood of the Lions scoring no goals in a game is: a. 0.95 b. 0.85 c. 0.75 d. None of the answers is correct.

6. In relation to Exhibit 5-5, the variance is: a. 1.431 b. 2.0475 c. 3.05 d. 21

7. Among the characteristics of a binomial experiment, which of the following is true? a. At least two outcomes are possible b. The probability of success varies from trial to trial c. The trials are independent d. All of these answers are correct.

8. The variance for the binomial probability distribution can be expressed as: a. Var(x) = p(1 − p) b. Var(x) = np c. Var(x) = n(1 − p) d. Var(x) = np(1 − p)

9. The standard deviation within a binomial distribution corresponds to: a. E(x) = pn(1 − n) b. E(x) = np(1 − p) c. E(x) = np d. None of the alternative answers is correct.

10. In a binomial experiment characterized by p = 0.5 and a sample size of 100, the expected value is: a. 0.50 b. 0.30 c. 50 d. Insufficient information for an answer.

11. Among a class of 100 students, 20% plan to attend graduate school. The corresponding standard deviation for this binomial distribution is: a. 20 b. 16 c. 4 d. 2

12. Pertaining to Exhibit 5-8, the variable being examined in this experiment is: a. the 60% of female students b. the random sample of 8 students c. the number of female students from the sample of 8 d. the size of the student body

13. According to Exhibit 5-10, the anticipated number of days Pete will successfully catch fish is: a. 0.6 b. 0.8 c. 2.4 d. 3

14. The binomial probability distribution achieves maximum symmetry when: a. n is 30 or greater b. n equals p c. p approaches 1 d. p equals 0.5

15. For any continuous random variable, the probability of it taking on a specific value is: a. 1.00 b. 0.50 c. any value between 0 to 1 d. zero

16. The peak of a normal curve occurs at: a. one standard deviation right of the mean b. two standard deviations right of the mean c. approximately three standard deviations right of the mean d. the mean

17. The standard deviation for a standard normal distribution: a. is always zero b. is always one c. can be any positive value d. can be any value

18. If Z is a standard normal random variable, then P(-1.5 ≤ z ≤ 1.09) equals: a. 0.4322 b. 0.3621 c. 0.7953 d. 0.0711

19. For a standard normal random variable z, what is its value if the area to the right is 0.1112? a. 0.3888 b. 1.22 c. 2.22 d. 3.22

20. In a standard normal random variable z, what is its value where the area to the right equals 0.1401? a. 1.08 b. 0.1401 c. 2.16 d. -1.08

21. For a standard normal distribution, the probability of obtaining a z value less than 1.6 is: a. 0.1600 b. 0.0160 c. 0.0016 d. 0.9452

22. According to Exhibit 6-5, the random variable in this case refers to: a. the weight of items produced by the machine b. 8 ounces c. 2 ounces d. the normal distribution

23. Referring to Exhibit 6-5, what percentage of the items will weigh between 6.4 and 8.9 ounces? a. 0.1145 b. 0.2881 c. 0.1736 d. 0.4617

24. Referring to Exhibit 6-6, the variable being assessed in this experiment is: a. the life expectancy of this tire brand b. the normal distribution c. 40,000 miles d. None of the alternative answers is correct.

25. From Exhibit 6-6, what is the probability that a randomly selected tire will last exactly 47,500 miles? a. 0.4332 b. 0.9332 c. 0.0668 d. zero

26. The term for standard deviation in relation to proportion is: a. standard proportion b. sample proportion c. average proportion d. standard error of the proportion

27. The standard deviation in relation to the mean is termed: a. standard x b. standard error of the mean c. sample standard mean d. sample mean deviation

28. A simple random sample of size n from a finite population of size N must be selected so that each possible sample of size: a. N has equal selection probability b. n has a 0.5 probability c. n has a 0.1 probability d. n has the same probability of being selected

29. If a population contains 500 elements, the probability of selecting an element in a simple random sample of 50 on the first draw is: a. 0.100 b. 0.010 c. 0.001 d. 0.002

30. A simple random sample of size n drawn from a finite population of size N must have: a. same probability of being selected b. a probability of 1/n of being selected c. a probability of 1/N of being selected d. a probability of N/n of being selected

31. A simple random sample from a process (infinite population) is selected under the condition that: a. each element belongs to the same population b. each element is drawn independently c. each element comes from the same population and is drawn independently d. probabilities for selection can vary

32. Among the following, which represents a point estimator(s)? a. σ b. μ c. s d. All of these answers are correct.

33. According to Exhibit 7-2, the point estimate of the proportion in the population responding "yes" is: a. 300 b. approximately 300 c. 0.75 d. 0.25

34. Referring to Exhibit 7-3, the point estimate of the population mean is: a. 18.0 b. 19.6 c. 108 d. sixteen, since 16 is the smallest value in the sample

35. The expected value for the random variable is: a. σ b. the standard error c. the sample size d. μ

36. Within a population of 500 elements, a sample of 225 is drawn. Knowing that the population's variance is 900, the standard error of the mean is approximately: a. 1.1022 b. 2 c. 30 d. 1.4847

37. Doubling the sample size will: a. reduce the standard error of the mean to half its current value b. reduce the standard error of the mean to about 70% of its current value c. have no impact on the standard error of the mean d. double the standard error of the mean

38. With a population mean of 84 and standard deviation of 12, the probability that the sample mean falls between 80.54 and 88.9 with a sample size of 36 is: a. 0.0347 b. 0.7200 c. 0.9511 d. None of the alternative answers is correct.

39. According to Exhibit 7-4, the standard error of the mean is: a. 0.3636 b. 0.0331 c. 0.0200 d. 4.000