A Collection of Multiple-Choice Cumulative Questions
In no Particular Order Answers are in Red
1. US Air has a flight to New York for $160 and United Airlines has a flight to New York for $200. Which
statement is true?
(A) The cost of the United flight is 25% more than US Air.
(B) The cost of the US Air flight is 80% less than the United flight.
answer:
A
answer:
A
(C) The cost of the United flight is 120% more than the US Air flight.
(D) The cost of the US Air flight is 25% less than United.
(E) The cost of the United flight is 20% more than US Air.
2. Which histogram below most closely depicts a normal distribution?
Histogram B
Histogram A
Histogram C
Histogram D
Histogram E
3. Suppose you could take all samples of size 64 from a population with a mean of 12 and a standard deviation
of 3.2. What would be the standard deviation of the sample means?
answer:
C
(A) 3.2
(B) 0.2
(C) 0.4
(D) 0.3
(E) 1.6
4. In a normally distributed variable, a value x∗ is considered unusually large if
(A) P (x ≤ x∗ ) < 0.05.
(B) P (x ≥ x∗ ) < 0.05.
answer:
B
∗
(C) P (x ≤ x ) > 0.05.
(D) P (x ≥ x∗ ) > 0.05.
(E) P (x = x∗ ) > 0.05.
5. A hypothesis test is conducted and the P -value of the test statistic is 0.02. Four of the following statements
are valid. Which statement is not valid.
(A) It is not very likely that the extremeness of the test statistic is due to chance.
(B) Assuming the null hypothesis is true, there is a 2% chance of getting a more
extreme test statistic.
(C) There is a 2% chance that the null hypothesis is false.
(D) At the 0.05 significance level, you would reject the null hypothesis.
(E) At the 0.01 significance level, you would fail to reject the null hypothesis.
answer:
C
6. Which of the following is NOT required of a binomial distribution
(A) Each trial has exactly two outcomes.
answer:
D
answer:
C
(B) There is a fixed number of trials.
(C) The probability of success remains fixed for all trials.
(D) There are more than 30 trials.
7. The mean = np and the standard deviation =
√
n p q for
(A) all probability distributions.
(B) normal distributions.
(C) binomial distributions.
(D) none of the above
8. The t distribution should be used to build confidence interval estimates of a population mean when the population standard deviation is
(A) small.
(B) 30 or more.
answer:
D
(C) too large to fit the normal distribution.
(D) unknown.
9. Which of the following is NOT a characteristic of the sampling distribution of sample means (the means of all
possible samples of a given size)?
(A) It is normally distributed.
answer:
C
(B) It is centered on the population mean.
(C) It has a standard deviation (σx̄ ) which is larger than the population standard deviation (σ).
(D) It has a standard deviation (σx̄ ) which is smaller than the population standard deviation (σ).
10. Which of the following is a possible alternative hypothesis H1 for a two-tailed test.
(A) µ < 30
(B) µ 6= 30
(C) µ = 30
(D) µ > 30
answer:
B
11. Suppose that at the 95% confidence level we calculate a confidence interval described by 43.8 < µ < 46.2.
Which of the following statements can not be made about this result.
(A) The sample mean is 45.
(B) The population mean is 45.
(C) The margin of error is 1.2.
(D) We are 95% confident that the population mean lies between 43.8 and 46.2.
answer:
B
12. Inferential statistics is so named because it allows us to examine a sample and make inferences about
(A) another sample.
answer:
C
answer:
D
(B) an element of the sample.
(C) the population from which the sample was taken.
(D) none of the above.
13. If the P-value of a given test statistic is 0.03 then,
(A) It is unlikely that the extremeness of the test statistic is due to chance.
(B) Assuming the null hypothesis is true, there is a 3% chance of getting a more extreme test statistic.
(C) At the 0.05 significance level, you would reject the null hypothesis.
(D) All of the above are viable conclusions.
14. The most frequently occurring value in a data set is called the
(A) mean.
(B) median.
(C) mode.
(D) range.
answer:
C
answer:
D
15. The median of a data set is also denoted by
(A) Q1
(B) Q3
(C) P2
(D) P50
16. A box of 8 marbles has 4 red, 2 green, and 2 blue marbles. If you select one marble, what is the probability
that it is a red or blue marble.
(A) 0.60
(B) 0.75
(C) 6.00
(D) 0.80
answer:
B
17. A box of 8 marbles has 4 red, 2 green, and 2 blue marbles. If you select two marbles, without replacement,
what is the probability that you select a red marble followed by a green marble.
(A) 0.0625
(B) 0.1250
(C) 0.1429
(D) 0.6000
answer:
C
18. Suppose a normally distributed random variable x has a mean of 100 and P (x < 90) = 0.40.
What is the probability that x is between 90 and 110? Ie. What is P (90 < x < 110)?
(A) 0.60
(B) 0.20
(C) 0.40
(D) 0.30
answer:
B
19. Suppose you are calculating the minimum sample size required for a confidence interval about a population
mean and you know σ. Which of the following does not influence the minimum sample size?
(A) the size of the population (N )
(B) confidence level (α)
(C) the acceptable margin of error (E)
(D) the size of the population standard deviation (σ)
answer:
A
A Collection of Past Questions Organized by Chapter
Chapter 1: Sampling, Levels of Measurement, Percentages
1. A random sample is one with which characteristic?
(A) Its members are chosen haphazardly.
answer:
(B) Every member of the population has an equal chance of being chosen for the sample.
(C) The population is divided into classes, and some members are chosen from each class.
(D) Every k th member of the population is chosen for the sample.
2. In a survey of 200 randomly selected Burlington residents, only 8% of them used public transportation. Which
of the following describes the population for this survey?
(A) The 200 Burlington residents selected for the survey.
(B) All Burlington residents.
answer:
(C) All Burlington residents who use public transportation.
(D) All Burlington residents who do not use public transportation.
3. US Air has a flight to New York for $160 and United Airlines has a flight to New York for $200. Three of the
following statements are true. Which statement is FALSE?
(A) The US Air flight costs 20% less than United.
(B) The United flight costs 25% more than US Air.
answer:
(C) The US Air flight costs 80% of the United flight.
(D) The United flight costs 80% more than the cost of US Air.
4. In a high-school with 200 males and 300 females, 50 students are needed for a study. The researchers decide
to randomly select 20 males and 30 females.
• This is an example which type of sampling method?
(a) systematic
(b) stratified
(c) cluster
• This sampling method is
(a) random but not simple random.
(d) None of these
(b) simple random.
(c) neither
answer:
answer:
5. Your social security number is an example of what level of measurement?
(A) Nominal
(B) Ordinal
(C) Interval
answer:
(D) Ratio
6. In an effort to determine the amount of debt for Champlain College students, I surveyed 100 students from
each class (Freshman, sophomore, junior, and senior). What method of sampling did I use?
(A) Stratified
(B) Systematic
(C) Cluster
answer:
(D) Convenience
Chapter 2: Descriptive Statistics
7. Which of the following is not a measure of center?
(a) standard deviation
(b) mean
(c) median
(d) mode
answer:
8. The median of a data set is also denoted by
(a) Q1
(b) Q3
(c) P2
(d) P50
answer:
9. Consider the data {10, 15, 20, 25, 30}.
Which of the following measures would not change if the 20 was replaced by a 25?
(A) The mean
(B) The median
answer:
(C) The mode
(D) The range
10. For the data {10, 15, 20, 25, 30}, which of the following measures not change if the 30 was replaced by a 40?
(A) The mean
(B) The median
answer:
(C) The standard deviation
(D) The range
11. Which of the following is not a measure of variation?
(A) The median
answer:
(B) The range
(C) The variance
(D) The standard deviation
12. In a normally distributed variable, those values more than 2 standard deviations away from the mean are
considered
(A) discrete.
(B) normal.
answer:
(C) impossible.
(D) unusual.
13. The symbol x represents
(A) the population mean
(B) the population standard deviation
answer:
(C) the sample mean
(D) the sample standard deviation
14. The most frequently occurring value in a data set is called the
answer:
(A) mean.
(B) median.
(C) mode.
(D) range.
Chapter 3: Tables and Graphics
15. Given the histograms below,
Histogram A
Histogram B
Histogram C
Histogram D
• which histogram most closely depicts a uniform distribution?
A) Histogram A
B) Histogram B
C) Histogram C
D) Histogram D
answer:
• which histogram most closely depicts a normal distribution?
A) Histogram A
B) Histogram B
C) Histogram C
answer:
• which histogram most closely depicts a skewed distribution?
A) Histogram A
B) Histogram B
C) Histogram C
D) Histogram D
answer:
D) Histogram D
16. A normal destribution can best be described as what?
(A) skewed
(B) flat
(C) symmetric and bell-shaped
(D) uniform
Chapter 4: Introduction to Probability
17. A box of 8 marbles has 4 red, 2 green, and 2 blue marbles. If you select one marble, what is the probability
that it is a red or blue marble.
(A) 0.60
(B) 0.75
(C) 6.00
(D) 0.80
answer:
18. A box of 8 marbles has 4 red, 2 green, and 2 blue marbles. If you select two marbles, without replacement,
what is the probability that you select a red marble followed by a green marble.
(A) 0.0625
(B) 0.1250
(C) 0.1429
(D) 0.6000
answer:
Chapter 5: Binomial Probability Distribution
19. A fair coin is tossed 10 times. What is the probability that of getting exactly 5 heads?
(a) 0.10
(b) 0.50
(c) 0.125
(d) 0.246
answer:
20. A fair coin is tossed 10 times. What is the probability that of getting less than 3 heads?
(a) 0.172
(b) 0.055
(c) 0.117
(d) 0.044
answer:
21. A binomial distribution consists of 150 trials. If the probability of success on each trial is 0.4, what is the
standard deviation of the distribution.
(a) 36
(b) 16
(c) 4
(d) 6
answer:
22. Which of the following is NOT required of a binomial distribution
(A) Each trial has exactly two outcomes.
answer:
(B) There is a fixed number of trials.
(C) The probability of success remains fixed for all trials.
(D) There are more than 30 trials.
23. The mean = np and the standard deviation =
√
n p q for
(A) all probability distributions.
answer:
(B) normal distributions.
(C) binomial distributions.
(D) none of the above
Chapter 6: Normal Distributions
24. If you got a 79 on a test in a class with a mean score of 85 and a standard deviation of 4.8, the z-score of your
test score would be
(a) 1.25
(b) -2.50
(c) -1.25
(d) 2.50
answer:
25. If the heights of women are normally distributed with a mean of 64 inches and a standard deviation of 1 inch,
the probability of randomly selecting a woman taller than 62.5 inches is
(a) 0.0668
(b) 0.9332
(c) 0.6195
(d) 0.9938
answer:
26. Suppose a normally distributed random variable x has a mean of 100 and P (x < 90) = 0.40.
What is the probability that x is between 90 and 110? Ie. What is P (90 < x < 110)?
(a) 0.60
(b) 0.20
(c) 0.40
(d) 0.30
answer:
27. Suppose you were to take samples of size 64 from a population with a mean of 12 and a standard deviation of
3.2. What would be the standard deviation of the sample means?
(a) 0.60
(b) 0.20
(c) 0.40
(d) 0.30
answer:
28. In a normally distributed variable, a value x∗ is considered an unusually large if
(A) P (x ≤ x∗ ) < 0.05.
(B) P (x ≥ x∗ ) < 0.05.
answer:
(C) P (x ≤ x∗ ) > 0.05.
(D) P (x ≥ x∗ ) > 0.05.
29. If the heights of women are normally distributed with a mean of 64 inches, which of the following is the highest?
The probability of randomly choosing
(A) one woman and finding her height is between 63 and 65 inches.
answer:
(B) 15 women and finding that their mean height is between 63 and 65 inches.
(C) 100 women and finding that their mean height is between 63 and 65 inches.
(D) all of the above have the same probability.
30. Which of the following is NOT a characteristic of the sampling distribution of sample means (the means of all
possible samples of a given size)?
(A) It is approximately normally distributed.
answer:
(B) It is centered on the population mean.
(C) It has a standard deviation (σx̄ ) which is larger than the population standard deviation (σ).
(D) It has a standard deviation (σx̄ ) which is smaller than the population standard deviation (σ).
31. Suppose a normally distributed random variable x has a mean of 100 and P (x < 90) = 0.20.
What is the probability that x is between 90 and 110? Ie. What is P (90 < x < 110)?
(a) 0.60
(b) 0.20
(c) 0.40
(d) 0.30
answer:
Chapter 7: Confidence Intervals
32. Suppose that at the 95% confidence level we calculate a confidence interval described by 43.8 < µ < 46.2.
Which of the following statements can not be made about this result.
answer:
(A) The sample mean was 45.
(B) The population mean is 45.
(C) The margin of error is 1.2.
(D) We are 95% confident that the population mean lies between 43.8 and 46.2.
33. Inferential statistics is so named because it allows us to examine a sample and make inferences about
(A) another sample.
answer:
(B) an element of the sample.
(C) the population from which the sample was taken.
(D) none of the above.
34. Which of the following factors would NOT influence the size of the margin of error (E), in a confidence interval
estimate of a population mean?
(A) the standard deviation
answer:
(B) the confidence level
(C) the sample size
(D) the size of the population
35. You want to estimate the proportion of American voters who are optimistic about the state of the economy.
How large a sample would be needed to ensure a 95% probability that the actual population proportion will
be no more than 3 percentage points from the sample population?
(A) 1506
(B) 1068
(C) 3152
(D) 938
answer:
Chapter 8: Hypothesis Testing - One Sample
36. Which of the following represents a parameter.
(a) µ
(b) s
(c) x̄
(d) p̂
answer:
37. In hypothesis testing the significance level α represents the probability of
(A) a Type I error.
(B) a Type II error.
answer:
(C) rejecting the null hypothesis when it is false.
(D) accepting the null hypothesis when it is true.
38. In hypothesis testing, the significance level α represents the probability of
(A) rejecting the claim.
(B) a Type I error.
answer:
(C) rejecting the null hypothesis when it is false.
(D) rejecting the alternate hypothesis when it is false.
39. Which of the following is a possible alternative hypothesis H1 for a two-tailed test.
(A) µ < 30
(B) µ 6= 30
(C) µ = 30
answer:
(D) µ > 30
40. If the P-value of a given test statistic is 0.03 then,
(A) It is unlikely that the extremeness of the test statistic is due to chance.
answer:
(B) Assuming the null hypothesis is true, there is a 3% chance of getting a more extreme test statistic.
(C) At the 0.05 significance level, you would reject the null hypothesis.
(D) All of the above are viable conclusions.
41. The symbol µ represents the
(A) population mean.
(B) sample mean.
answer:
(C) population standard deviation.
(D) significance level.
42. If the P-value of a given test statistic is 0.18 then,
(A) It is quite possible that the extremeness of the test statistic is due to chance.
answer:
(B) Assuming the null hypothesis is true, there is an 18% chance of getting a more extreme test statistic.
(C) At the 0.05 significance level, you would fail to reject the null hypothesis.
(D) All of the above are viable conclusions.
43. The P -value is
(A) the probability of rejecting the null hypothesis when it is true.
(B) the probability that the claim is true.
answer:
(C) the estimate of the population parameter given the sample statistic.
(D) the probability of getting a test statistic more extreme than the one you got assuming the null hypothesis
is correct.
44. You test a claim that more than 10% of adults have tatoos. Your test statistic turns out to be zp̂ = 2.31.
What is the P -value of this test statistic?
(A) 0.9896
(B) 0.0104
answer:
(C) 0.0208
(D) 0.0951
45. Which of the following alternate hypotheses is indicative of a two tailed test.
(A)
H1 : µ < 100
(B)
H1 : µ = 100
(C)
H1 : µ 6= 100
(D)
H1 : µ > 100
answer:
46. If you want to conduct a hypothesis test about a mean from a population with a skewed distribution, you
should
(A) use a stratified sample.
(B) use a large significance level.
answer:
(C) have all outcomes classified as success or failure.
(D) use a sample size greater than 30.
47. For hypothesis tests about a mean, you should use a sample size greater than 30 when
(A) the population distribution is not normal.
(B) the P -value is less than α.
answer:
(C) the population size is large.
(D) the significance level is greater than 0.01.
Chapter 10: Correlation and Regression
48. I found a significant correlation between the time it takes students to complete an exam and the score on the
exam. The regression equation is given by
ŷ = 2.5 x − 10.2
where y is the score on the exam and x is the completion time (in minutes). Is this a positive or negative
correlation?
(A) Positive Correlation
answer:
(B) Negative Correlation
49. Many studies have shown that students score higher on math tests when there is classical music playing in the
background. Identify the response variable.
(A) Math test scores
answer:
(B) classical music in the background
50. If we fail to find a significant linear relationship between two variables, then the best prediction for any value
of x would be found by using what?
(A) regression equation
(B) average x-value
(C) average y-value
(D) the slope of the regression line
answer: