Download Indicate whether the sentence or statement is true or false

PBL Quantitative Methods
2002 NLC
Indicate whether the sentence or statement is true or false. Mark "A" if the statement is
True or "B" if it is False.
1. The standard deviation is sometimes negative.
2. Random assignment is a method of controlling, for selection threat.
3. The larger the sample size, the more difficult it is to find significance.
4. A sample is a target population to which a researcher intends to generalize the results.
5. Scores with the smallest effect on the mean are considered outliers.
6. A correlation coefficient may not always demonstrate a relationship between variables even
though a strong relationship exists.
7. If all of the values in a data set are100, then the standard deviation is also 100.
8. Histograms are sometimes manipulated to make the data appear more attractive.
9. A sample of volunteers is unbiased because they are representative of the total population.
10. With a simple random sample, choosing one subject increases the possibility of another
subject being chosen.
11. A secondary analysis is a study in which the researcher reanalyzes data gathered by a
previous researcher to test an alternative researcher hypothesis.
12. The ordinal level of measurement assigns numbers to different categories (e.g., MALE=1
and FEMALE =2).
Mark the correct answer on your scantron sheet for each of the following questions.
13. The midrange is defined to be the smallest plus the highest value divided by two. The
midrange
a. is a measure of center.
b. is a measure of variability.
c. is usually bigger than the mean.
d. has more information than the average.
14. Which of the following is true about the distribution of fish in the ocean?
a. It has shifted to the left in the last fifty years.
b. It has shifted to the right in the last twenty years.
c. It has an average that has increased in the last twenty-five years.
d. It is better represented by the midrange than the median.
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15. All of the following measure variability, except for the
a. variance.
b. highest value - the lowest value.
c. highest value + the lowest value.
d. interquartile range.
16. The empirical rule is derived from which of the following distributions?
a. The binomial distribution
b. The F distribution
c. The normal distribution
d. The t distribution
17. A symmetric distribution
a. has a bigger standard deviation than a skewed distribution.
b. usually has a negative mean.
c. has a mean equal to the median.
d. cannot determine the relationship between the mean and median.
Use class sizes of 0-19, 20-39, to answer questions 18 to 20.
The number of pages of textbooks read by a number of students last week is given below:
110, 50, 25, 20, 76, 10, 0, 52, 88, 80, 37, 19, 133, 62, 113, 120, 13, 200, 18, 44.
18. What is the frequency associated with the class 20-39?
a. .15
b. 3
c. 4
d. 15%
19. What is the relative frequency associated with the class 0-19?
a. .25
b. 5
c. 6
d. 40%
20. What percent of the data is between 80 and 210?
a. 30%.
b. 35%.
c. 40%.
d. 65%.
21. A histogram is better than a bar graph for
a. bivariate data.
b. binomial data.
c. qualitative data.
d. quantitative data.
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22. The average for the data: 4, 5, 7, 12, 12, 14 is
a. 7.
b. 7.5.
c. 9.
d. 12.
23. The median for the data: 4, 5, 7, 12, 12, 14 is
a. 7.
b. 9.
c. 9.5.
d. 11.
24. The sample standard deviation for the data: 4, 5, 7, 12, 12, 14 is
a. 4.20.
b. 4.08.
c. 3.83.
d. 3.76.
25. The 50th percentile for the data: 4, 5, 7, 12, 12, 14 is
a. 7.
b. 9.
c. 9.5.
d. 12.
26. A histogram
a. cannot be used on quantitative data.
b. is almost always skewed to the right.
c. represents positive numbers better than negative numbers.
d. Is a useful picture for summarizing data.
27. Which of the following is true about sampling?
a. Sampling from a finite population is more accurate than from an infinite population.
b. Sampling from an infinite population is more accurate then from a finite population.
c. Sampling from infinite and finite populations has the same accuracy.
d. All of the above.
28. A z-score
a. measures the skewness of a distribution.
b. is the number of standard deviations a data point is from the mean.
c. is usually bigger than the corresponding t-score.
d. is never used with the binomial distribution.
29. A population has a mean of 150 and a standard deviation of 50. A data point of 200
a. is unusually high.
b. is impossible.
c. is unusually low.
d. is not unusual.
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30. A variable X has a uniform distribution from 2 to 10. The 70-th percentile for X is
a. 5.0.
b. 6.5.
c. 7.6.
d. 8.1.
31. Suppose you know that a population has a mean of 100 with a standard deviation of 20.
Suppose also a random sample of size 25 is taken from this population and the sample
average is computed. The distance between the sample average and 100 should be about
a. 25.
b. 20.
c. 10.
d. 4.
32. A population has a mean of 200 and a standard deviation of 40. A z-score of 1.5
corresponds to a data point of
a. 300.
b. 260.
c. 220.
d. 140.
33. Which of the following is not true about the t-distribution.
a. It is used with the population standard deviation.
b. It can have more than 60 degrees of freedom.
c. It is used with the sample standard deviation.
d. It is symmetric about zero.
34. Non-Response bias is
a. not finding people at home.
b. people who do not respond immediately and have to think before answering.
c. people who give incorrect answers on purpose over the phone.
d. all of the above.
35. Gerald drinks one cup of coffee per day with probability .1, two cups per day with probability
.2, three cups per day with probability .3, and four cups with probability .4. The conditional
probability that Gerald drinks at least three cups of coffee on a given day, given that he has
drunk at least two cups of coffee on that day, is
a. .3.
b. .9.
c. .666667.
d. .777778.
36. When reporting the income of a locality, it is best to use median income because the
a. median controls for outliers.
b. median over-inflates income, making it appear higher.
c. median does not account for individuals making less than $20,000 per year.
d. mean is actually the better descriptive statistic for reporting income.
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37. The sample average of 100 observations from an unknown population has
a. the same accuracy as one observation.
b. twice the accuracy as one observation.
c. ten times the accuracy as one observation.
d. one hundred times the accuracy as one observation.
38. Gerald drinks one cup of coffee per day with probability .1, two cups per day with probability
.2, three cups per day with probability .3, and four cups with probability .4. The mean
number of cups of coffee per day is
a. 2.
b. 2.5
c. 3.
d. 3.5
39. A fair die is rolled twice. The probability that the sum of the rolls is two, is 1/36. The
probability that the sum is 3, is 2/36. If x is the sum, then the discrete probability density
function is given by
a. (x-1)/36.
b. (1-x)/36.
c. 6/36-|x-7|/36.
d. none of the above.
40. A researcher is studying the relationship between height and weight. The best graphical
method for this problem would be a
a. bar graph.
b. histogram.
c. stem and leaf plot.
d. scatter plot.
41. Janet has a 40% chance of seeing a robin in the tree outside her window in the morning. In
five mornings, the chance she sees a robin on four of the mornings is
a. .0388.
b. .0768.
c. .0968.
d. .1104.
42. Data was collected on the number of American flags sold per day at a large department
store. Over twenty-five days the average number of flags sold per day was 222. If the
population standard deviation is 30 flags per day, a 90% confidence interval for the true
average number of flags sold per day is
a. 231.87.
b. 232.27.
c. 233.76.
d. 234.38.
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43. A tire manufacturer can make the same tire by two different processes. The process with
the least volatility would be preferred because consistency is preferred in quality control.
After the data is collected, which hypothesis test should be carried out?
a. Z-test
b. T-test
c. Chi-square test
d. F-test
44. A wife believes that her husband usually spends more than three hours fishing whenever he
goes fishing. To prove her wrong, he collects data and, in twenty-five trips spent, on
average,182 minutes fishing with a standard deviation of 30 minutes. With a null hypothesis
 <= 180, an alternative hypothesis  > 0, and  = .10, a hypothesis test would suggest
a. it is impossible to tell.
b. neither is correct.
c. the wife is correct.
d. the husband is correct.
45. A teacher is predicting the final exam score from the midterm exam score, with SX =20, SY
=20 and r = .5. If b is the slope coefficient then the value of the coefficient b is
approximately
a. 0.
b. .5.
c. 1.
d. 2.
46. An accounting firm is auditing the books of a company. The accounting firm takes the null
hypothesis that the company has given them correct information. A Type II error is
interpreted as the fact that the accounting firm believes the company has given them
a. correct information, when the company really has given them correct information.
b. incorrect information, when the company really has given them correct information.
c. incorrect information, when the company really has given them incorrect information.
d. correct information, when the company really has given them incorrect information.
47. A new restaurant wants to determine how many customers they serve on average per day.
The standard deviation is expected to be 70 customers per day. If they want to know, to
within 10 customers per day, with 95% probability how many days must they collect data
on?
a. 70
b. 95
c. 133
d. 189
48. In a group of students, the correlation coefficient between height and weight should be
about
a. -.5.
b. 0.
c. .5.
d. 1.
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49. A regression model of the form Y = a + b*X is fit resulting in the regression equation Y = 2 +
7.5X. If n=100, SD(b) = 2, and  = .10 then
a. X is a significant negative predictor of Y.
b. X is a significant predictor of Y.
c. X is not a significant predictor of Y.
d. there is not enough information to say anything.
50. A company that is located downtown in a large city wants to predict how long its employees
commute to work. Three predictors are used in a multiple regression model with Y = time
to commute, X1 = distance from work, X2 = age of the employee, X3 = 1 if the commute is
by car and 0 if the commute is by public transportation. The pvalue for the test of b1 is
.001, the pvalue for the test of b2 is .951, the pvalue for the test of b3 is .002, and the
pvalue for the F-test of the whole model is .0003. Which of the following is not true?
a. All variables are relevant.
b. At least two variables are relevant.
c. At least one of the variables is relevant.
d. b1 = positive, b3 = negative.
51. In a multiple regression Y = a + b1X1 + b2X2, the correlation between Y and X1 is .4 and
the correlation between Y and X2 is .5. The percent of explained variance is
a. .4 + .5.
b. .92.
c. .42 + .52.
d. not known because there is not enough information to tell.
52. The law of large numbers says that
a. large data points strongly affect the sample average.
b. for large amounts of data, the sample average will be close to the population average.
c. for large amounts of data, the t-curve is close to the normal curve.
d. a large confidence interval is good for data analysis.
53. One example of a measure of dispersion (or variability) is
a. mean.
b. percentile.
c. standard deviation.
d. median.
54. Subtracting the lowest score from the highest score and adding 1 will determine the
a. range.
b. median.
c. mode.
d. standard deviation.
55. A rank at the 50th percentile on an achievement test indicates that
a. this person failed the test.
b. the raw score was a 50 out of 100 possible points.
c. this person guessed on at least half of the items.
d. this person did as good, or better than, half of the students who took the same test.
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56. The median is always
a. an actual raw score.
b. at the 50th percentile.
c. larger than the mean.
d. the same as the arithmetic average.
57. The percentage of normally distributed scores that fall between one standard deviation
above and below the mean is
a. 98%.
b. 68%.
c. 50%.
d. 14%.
58. In a perfect normal distribution of scores, the mean will equal a percentile rank of
a. 98%.
b. 68%.
c. 50%.
d. 14%.
59. A z score is considered a
a. measure of related position.
b. measure of dispersion.
c. measure of association.
d. measure of central tendency.
60. A rank at the 70th percentile would be equal to a quartile rank of the
a. 1st quartile.
b. 2nd quartile.
c. 3rd quartile.
d. 4th quartile.
61. A rank at the 5th percentile would be equal to a decile rank of the
a. 1st decile.
b. 2nd decile.
c. 3rd decile.
d. 4th decile.
62. Failing to reject the null hypothesis when the null is false is called
a. a Type I error.
b. a Type II error.
c. a small effect size.
d. sufficient power.
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63. With all factors held constant, increasing sample size will
a. increase power.
b. decrease power.
c. have no effect on power.
d. skew power to the right.
Use the following information for questions 64-67.
College Board test scores have a population mean of 500 and standard deviation of 100.
Suppose a random sample of 64 is taken from this population.
64. The sampling distribution of the mean has a mean of
a. 640.
b. 564.
c. 500.
d. 436.
65. The sampling distribution of the mean has a standard deviation (standard error of the mean)
of
a. 50.00.
b. 25.00.
c. 20.25.
d. 12.50.
.
66. If the sample size were increased, the mean of the sampling distribution would
a. increase.
b. decrease.
c. stay the same.
d. become prone to Type II error.
67. If the sample size were increased, the standard error of the mean would
a. increase.
b. decrease.
c. stay the same.
d. become prone to Type II error.
Use the following information for questions 69-71
Variable X is known to be negatively skewed with a mean of 150 and a standard deviation of
25. For a research study, a sample mean of 25 individuals is randomly selected.
68. The sampling distribution of the mean has a mean of B
a. 175.
b. 150.
c. 125.
d. 100.
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69. The sampling distribution of the mean has a standard deviation (standard error of the mean)
of
a. 5.
b. 25.
c. 10.
d. 2.5.
70. The sampling distribution of the mean is
a. negatively skewed.
b. positively skewed.
c. rectangular.
d. normal.
Use the following information to answer questions 71-74
A smoker has 10 pipes. Three of them are black. Six of the pipes are curved, two of which are
black. He asks his son to bring him a pipe. The boy picks a pipe at random.
71. What is the probability he will pick a black pipe?
a. .5
b. .4
c. .3
d. .2
72. What is the probability he will select a black pipe or a curved stem pipe?
a. .7
b. .6
c. .5
d. .4
73. Later, he gives his son the pipe to return to the collection and asks for a second pipe. His
son again selects randomly. What is probability that both of the pipes (the original and the
new one) are black?
a. .12
b. .09
c. .06
d. .03
74. If he keeps the first pipe and asks for a second one, what is the probability that both pipes
are black?
a. .075
b. .067
c. .045
d. .023
75. Which of the following is the strongest correlational coefficient?
a. .85
b. .20
c. -.25
d. -.87
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76. Many universities have institutional review boards. The main function of an institutional
review board is to
a. determine procedures for allowing institutionalized individuals to participate in research
studies.
b. review research proposals to ensure that they provide satisfactory protection of human
subjects.
c. review research proposals to ensure that the research will yield useful results for the
sponsoring institution.
d. review completed research studies to ensure that human subjects were adequately
protected.
Use the following information for questions 77-81
A study was conducted to determine whether computerized tutorials help high schools students
in business math. Students enrolled in business math at a Floyd County High School and at a
Roanoke County High School both received the same pre-test and post-test. However, the
students at the Roanoke County High School did not receive the computerized tutorials. At the
end of the course, the students in Floyd County received higher scores on the post-test. The
post-test was a final exam.
77. What was this research study’s dependent variable?
a. Raw score on pre-test
b. Raw score on post-test
c. Whether or not they took the tutorial
d. The county the high school was located in
78. What was this research study’s independent variable?
a. Raw score on pre-test
b. Raw score on post-test
c. Whether or not they took the tutorial
d. The county the high school was located in
79. Which of the following statements is true?
a. A random assignment was used in this study.
b. Because a pre-test was used, a random assignment was unnecessary.
c. This research study was a true experiment.
d. Intact groups are more convenient to use than random assignment.
80. What level of measurement was used for the post-test?
a. Ordinal
b. Nominal
c. Interval
d. Ratio
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81. Which of the following statements could be considered a threat to external validity in this
study?
a. Half of the students in the business math class in Roanoke County became ill during the
final exam.
b. Ten new students moved into Roanoke County during the research study.
c. There were preexisting differences in intelligence between the two groups.
d. Students in Roanoke and Floyd may be different from students elsewhere.
Use the following information to answer questions 82 & 83
A recent research study concerning weight loss was conducted over a four-month period.
Participants were randomly assigned into one of four groups. The first group maintained their
normal diet, but exercised for two hours, five times a week. The second group had a high
protein, low carbohydrate diet over the four-month period. The third group skipped one meal a
day and drank diet-shakes as a replacement. The fourth groups maintained their normal diets.
82. Which of the following groups was the control group?
a. Group 1
b. Group 2
c. Group 3
d. Group 4
83. What would the null hypothesis be for this research study?
a. There will be no difference in the group means.
b. All of the group means will be significantly different.
c. One of the group means will be significantly different from the rest.
d. At least one of the group means will be significantly different from at least one other of
the group means.
84. All of the following are considered characteristics of experimental research except the
a. researcher manipulates or controls an independent variable.
b. number of subjects must exceed 100 individuals.
c. subjects are randomly selected from a population.
d. subjects are randomly assigned to an experimental or control group.
85. In a carefully controlled experimental study, statistically significant differences found
between the experimental group and the control groups are attributed to the differing
manipulation of the
a. dependent variable.
b. intervening variable.
c. extraneous variable.
d. independent variable.
86. Those proxy variables that determine the assignment of subjects to a particular group are
referred to as
a. treatment independent variables.
b. intervening independent variables.
c. organismic or attribute independent variables.
d. extraneous independent variables.
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87. A researcher is attempting to find out whether Test A is correlated to some other accepted
test. This researcher is concerned with
a. validity.
b. reliability.
c. mortality.
d. congruence.
88. A correlation of -1.00 indicates
a. a perfect positive relationship.
b. a strong negative relationship.
c. a perfect negative relationship.
d. a weak positive relationship.
89. Selecting every 10th subject from an accurate and finite list of a population is an example of
which sampling method?
a. Cluster random sampling
b. Simple random sampling
c. Stratified random sampling
d. Systematic sampling
90. One major disadvantage of a non-probability sample is that
a. subjects may not represent the greater population.
b. participating in the study may be inconvenient for the student.
c. it consumes a considerable amount of time to randomly select the subject from the
population.
d. there are no disadvantages.
Use the following information to answer questions 91-94
Assume that you have bought a raffle ticket for a local charity and that your sister
has bought three tickets. You have just read that 800 tickets have been sold.
91. What is the probability that you will win the grand prize?
a. .00150
b. .08000
c. .01750
d. .00125
92. What is the probability that your sister will win the grand prize?
a. .00275
b. .00375
c. .00830
d. .08300
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93. What is the probability that you or sister will win the second prize after someone else won
the grand prize?
a. .005
b. .006
c. .007
d. .075
94. Which of the following situations is the best example of joint probability?
a. The likelihood a person will be wearing a seatbelt and have a driver's side airbag
b. The likelihood a person will be in an accident after drinking alcohol
c. The likelihood a person will be wearing their seatbelt after they have been drinking
alcohol
d. The likelihood a person will purchase a car with a driver's side airbag after being in an
accident
95. In order to establish that factor A causes factor B to occur, the researcher must
a. identify occurrences of factor B in a control group compared with an experimental group.
b. ensure that the subjects in the control group and experimental group are essentially
equal in all salient characteristics.
c. introduce factor A to the experimental group only.
d. do all of the above.
96. An important method of challenging or verifying the conclusions of a previous study is
known as
a. replication.
b. meta-analysis.
c. secondary analysis.
d. follow-up analysis.
97. All of the following are primary sources of data except
a. documents recording events by actual participants.
b. biographical accounts of events.
c. oral testimonies from actual witnesses.
d. remains of objects from a specific time period.
98. A researcher concluded that a person with a college degree makes $40,000 a year, while
someone lacking a high school diploma makes $20,000 a year. In the study, which level of
measurement was used for the dependent variable?
a. Nominal
b. Interval
c. Ordinal
d. Ratio
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2002 PBL QUANTITATIVE METHODS ANSWER KEY
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
16.
17.
18.
19.
ANSWER
B
A
B
A
B
A
B
A
B
B
A
B
A
A
C
C
C
B
A
26.
27.
28.
29.
30.
31.
32.
33.
34.
35.
36.
37.
38.
39.
40.
41.
42.
43.
44.
ANSWER
D
A
B
D
C
D
B
A
A
C
A
C
C
C
D
B
A
D
D
51.
52.
53.
54.
55.
56.
57.
58.
59.
60.
61.
62.
63.
64.
65.
66.
67.
68.
69.
ANSWER
D
B
C
A
D
B
B
C
A
C
A
B
A
C
D
B
B
B
A
76.
77.
78.
79.
80.
81.
82.
83.
84.
85.
86.
87.
88.
89.
90.
91.
92.
93.
94.
20.
21.
22.
23.
24.
25.
B
D
C
C
A
C
45.
46.
47.
48.
49.
50.
B
D
D
C
B
A
70.
71.
72.
73.
74.
75.
D
C
A
B
B
D
95.
96.
97.
98.
99.
100.
ANSWER
B
B
C
D
C
D
D
A
B
D
C
A
C
A
A
D
B
A
A
D
A
B
D
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