Download STAT 100, Section 4 Sample Final Exam Questions, part I Fall 2008

STAT 100, Section 4
Sample Final Exam Questions, part I
The following questions are similar to the types of questions you will see on the final
exam. The actual final will consist of 70 to 80 multiple-choice questions.
NOTE: On the actual exam, the choices will not require calculator math.
On this sample exam, some of the choices may require a calculator.
Question 1. Fiona receives a beautiful four-sided die for her eighteenth birthday. After
playing with it for two hours, she starts to suspect that her die is more favorable
to rolling “1” than to any other number. Fiona chooses for her test statistic the
standardized score corresponding to the sample proportion of 1’s obtained in 300 rolls
of her die. The standardized score is
Sample proportion - Population proportion
S.D. of the sample proportion
Fiona rolled her die 300 times and obtained a “1” on 93, or 31%, of her rolls.
The value of Fiona’s test statistic is:
(A) q 0.31−0.25
= 2.4
(B) q 0.25−0.31
= -2.4
(C) q 0.31−0.25
= 2.25
(0.25)(1−0.25)
300
(0.25)(1−0.25)
300
(0.31)(1−0.31)
300
(D) q
300−93
(0.25)(1−0.25)
300
= 8,280
Question 2. In a randomized experiment, if the p-value is small when comparing the
treatment and control groups, we can infer that the treatment caused the difference:
(A) True
(B) False
Question 3. A researcher repeatedly collects random samples of size 1,600 and computes
a 95% confidence interval for the population mean using each sample. Over the long
run, the proportion of confidence intervals which will fail to capture the population
mean is:
(A) None of the above.
√
(B) 1/ 1, 600, or 1/40, 2.5%
(C) 95%
(D) 5%
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Fall 2008
Question 4. A research experiment found that ABC bubblegum retains its flavor longer
than XYZ bubblegum. We then know that:
(A) the p-value was small
(B) they must have committed a Type 1 error
(C) the p-value was large
(D) they must have committed a Type 2 error
Question 5. A confidence interval for a population mean is given as “Sample mean ±
2.33×SEM.” The corresponding level of confidence is:
(A) 98%
(B) 99%
(C) 95%
(D) 64%
Question 6. The following table shows some data summaries for amount of change carried
by people in a sample taken from class.
Men Women
Mean
59
82
smallskip
SEM
9
12
SD of difference
15
To test the research hypothesis that women carry more change than men, we must compute
the test statistic:
(A)
(B)
(C)
(D)
59
82
9 + 12 = 13.39
59+82
15 = 9.40
82
59
9 − 12 = −0.28
59−82
15 = −1.53
Question 7. A random sample of 25 farmers was examined in a study of caffeine levels.
From the data collected, a 95% confidence interval for the population mean caffeine
level was calculated to be 21.5 to 23.0. We can conclude that:
(A) If we repeatedly collect random samples of size 25 and calculate the corresponding
confidence intervals then, over the long run, 95% of these intervals will capture the
population mean and 5% will fail to capture the population mean.
(B) For any random sample of 25 farmers, the resulting sample mean will always fall
between 21.5 and 23.0.
(C) If we repeatedly sample the entire population then, about 95% of the time, the
population mean will fall between 21.5 and 23.0.
(D) None of the above.
(E) 95% of all farmers have caffeine levels between 21.5 and 23.0.
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Question 8. A p-value is a probability that is computed under what assumption?
(A) The alternative hypothesis is true
(B) A type 2 error has been committed
(C) A type 1 error has been committed
(D) The null hypothesis is true
Question 9. A sample of 28 temperature measurements in ◦ F, all taken at 12:00 p.m.,
was collected in a coastal town in NC. The data are given in the following stemplot:
Stemplot of Temperature Readings
3
5
6
7
8
9
2
5
0
3
0
0
1
5
0
2
2
5
2
3
4
6
3
5
48
8899
458
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For the data given in this stemplot, the five-number summary is:
(A) 55, 66, 78.5, 84.5, 95
(B) 32, 68, 79, 88, 98
(C) 32, 66, 78.5, 84.5, 98
(D) 32, 66, 78, 84, 98
Question 10. In a study to determine if putting newborn babies in an incubator contributed to claustrophobia in adult life, the researchers found a p-value of .023. This
study supports:
(A) both the skeptic and the research advocate
(B) the research advocate
(C) the skeptic
(D) neither the skeptic nor the research advocate
Question 11. In a study of PSU students’ awareness of world issues, a television crew
sampled students sitting in the Hub at 12:00 p.m. (noon). This survey is an example
of:
(A) A simple random sample, because it is simple to find students at the Hub in a random
manner.
(B) A haphazard (or convenience) sample, because the Hub is a convenient place to find
students.
(C) A stratified random sample, because students are stratified by gender and they are
found at the Hub in a random manner.
(D) A volunteer response sample because, to be seen on the evening news, students will
eagerly volunteer their responses.
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Question 12. During lunch today, I found a shiny new dime! To study the problem of
whether the coin is fair, I choose as my test statistic the number of heads obtained in
20 tosses. When I tossed the coin 20 times, I obtained 13 heads. Bearing in mind that
the probability of 13 or more heads in 20 tosses of a fair coin is 13.16%, my decision
is to:
(A) Fail to reject the null hypothesis: I do not have strong evidence against the hypothesis
that the coin is unfair.
(B) Fail to reject the null hypothesis: I do not have strong evidence against the hypothesis
that the coin is fair.
(C) Reject the null hypothesis: I have strong evidence against the hypothesis that the coin
is unfair.
(D) Reject the null hypothesis: I have strong evidence against the hypothesis that the
coin is fair.
Question 13. A radio advertiser wishes to choose a sample of size 100 from a population
of 5000 listeners. He divides the population into a large number of groups. He selects
a simple random sample of the groups and then surveys every subject in each of the
groups selected. This method of random sampling is called:
(A) Cluster sampling.
(B) Random digit dialing.
(C) Stratified random sampling.
(D) Systematic random sampling.
Question 14. Consider the research hypothesis: Working at least 5 hours per day at a
computer contributes to deterioration of eyesight. The alternative hypothesis is:
(A) Working at least five hours a day at a computer improves eyesight.
(B) Working at least five hours a day at a computer contributes to deterioration of eyesight.
(C) Insufficient information is given to allow us to determine the alternative hypothesis.
(D) Working at least five hours a day at a computer does not contribute to the deterioration
of eyesight.
Question 15. All other things remaining constant, if the sample size increases by a factor
of 25 then the standard error of the mean:
(A) Becomes one twenty-fifth as large.
(B) Becomes five times as large.
(C) Becomes one fifth as large.
(D) Becomes twenty-five times as large.
(E) Will remain unchanged.
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Question 16. To test the effects of sleepiness on driving performance, twenty volunteers
took a simulated driving test under each of three conditions: Well-rested, Sleepy, and
Exhausted. The order in which each volunteer took the three tests was randomized,
and an evaluator rated their driving accuracy without knowing the condition of the
volunteer. This type of experiment is a:
(A) Single-blind, matched-pair experiment.
(B) Single-blind, block design experiment.
(C) Retrospective observational study.
(D) Double-blind, matched-pair experiment.
Question 17. Hypothetical research question, asked of a random sample of students: Do
you own a pet? (Data and related output below.)
Female
Male
All
Chi-sq =
No Pet
26
17
43
Yes Pet
50
18
68
All
76
35
111
0.40 +
0.87 +
0.25 +
xxxx =
2.08
In the table above, the expected number corresponding to 18 is about:
(A) 17
(B) 111
(C) 21
(D) 68
(E) 14
Question 18. The importance of randomized experiments is that they:
(A) Require only small sample sizes.
(B) Allow the statistician to assign units to the treatment group.
(C) Allow the inference of causation.
(D) None of the above.
Question 19. In a random sample of 1,600 PSU students, 64% reported a preference
for root beer (over birch beer). In estimating the population proportion of all PSU
students who prefer root beer, we measure the precision of the sample proportion by:
(A) The square of the sample size: 1, 6002 , or 960, 000.
(B) The sample size as a proportion of all PSU students: 1, 600/82, 000, or 1.95%.
(C) The sample proportion: 64%.
√
(D) The margin of error: 1/ 1, 600, or 2.5%.
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Question 20.
which:
A confidence interval for a population proportion is a range of numbers
(A) Has a 90% probability of containing the population proportion.
(B) Increases in width as the sample size increases.
(C) Is certain to contain the population proportion.
(D) Is a plausible range of values for the population proportion.
Question 21. A sudy of PSU students failed ( p-value = .32) to find a difference in pulse
rates between men and women. Which of the following is true?
(A) The research hypothesis is supported
(B) It is possible that they committed a Type 2 error
(C) The null hypothesis is rejected
(D) It is possible that they committed a Type 1 error
Question 22. A radio advertiser wishes to choose a sample of size 100 from a population
of 5000 listeners. He divides the population into five separate groups and then selects
a simple random sample from each group. This method of sampling is called:
(A) Simple random sampling.
(B) Systematic random sampling.
(C) Volunteer sampling.
(D) Stratified random sampling.
Question 23. Suppose after viewing the results of a study you decide, on the basis of the
reported p-value, to support the skeptic. Then
(A) It is impossible for you to have committed either a Type 1 or Type 2 error
(B) It is impossible for you to have committed a Type 1 error
(C) You must have committed a Type 1 error
(D) It is impossible for you to have committed a Type 2 error
Question 24. In a study of the relationship between handspan (in centemeters) and height
(in inches) it was found that the correlation is about .80 and the regression equation
is
handspan = −3 + 0.35 height
What is the predicted handspan for someone 5 feet tall?
(A) 22.2 centimeters
(B) 3 centimeters
(C) 60 centimeters
(D) 18 centimeters
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Question 25. A study was conducted to see if PSU students sleep fewer than 8 hours.
The study was based on a sample of 100 students. The sample mean number of hours
of sleep was 7 and the SD was 5 hours. What is the p-value? (Hint: The test statistic
is very easy to compute here without a calculator.)
(A) .975
(B) .95
(C) .05
(D) .025
Question 26. The histogram of sample means from a large number of equally-sized
random samples of size 50 will be shaped approximately like a:
(A) Semi-circle.
(B) Skewed histogram, with a long right tail.
(C) Triangle.
(D) Normal (bell-shaped) curve.
Question 27. The Gallup Poll, a well-known polling group, regularly surveys the public on many issues. The number of interviews on which their surveys are based is,
approximately:
(A) 60,000 – 120,000
(B) 60–120
(C) 600,000 – 1,200,000
(D) The entire U.S. population.
(E) 600 – 1,200
Question 28. A simple random sample of ten subjects from a population is one in which:
(A) Any group of ten subjects has the same chance of being the selected sample.
(B) A simple way was found to choose ten subjects at random from the population.
(C) Most, but not all, groups of size ten have the same chance of being selected.
(D) We record the data provided by the first ten subjects who respond to the survey.
Question 29. The Empirical Rule states, in part, that if a data set is approximately
normally distributed (or bell-shaped) then:
(A) At most 90% of all observations fall within three standard deviations of the mean.
(B) About 37% of all observations fall within two standard deviations of the mean.
(C) About 68% of all observations fall within one standard deviation of the mean.
(D) None of the above.
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Question 30. All other things remaining constant, if the sample size decreases then the
standard error of the sample mean:
(A) Decreases.
(B) Increases, levels off, and then increases again.
(C) Increases.
(D) Will remain unchanged.
(E) Decreases and then increases.
Question 31. To test the effects of sleepiness on driving performance, twenty volunteers
took a simulated driving test under each of three conditions: Well-rested, Sleepy, and
Exhausted. The order in which each volunteer took the three tests was randomized,
and an evaluator rated their driving accuracy without knowing the condition of the
volunteer. The explanatory variable is:
(A) The order in which the volunteers took the tests.
(B) The condition of sleepiness.
(C) The evaluator’s rating of the driver’s condition.
(D) The evaluator’s rating of driving accuracy.
Question 32. A fair die if rolled repeatedly until the first six appears. What is the
probability that the first six appears on the fourth roll?
(A) ( 56 )6 = .3349
1
5
6 × 6 = .4167
5
5
5
1
6 × 6 × 6 × 6 = .0965
4
6 = .6667
(B) 3 ×
(C)
(D)
Question 33.
In an example in the textbook, the correlation between wives’ and husbands’ heights, in
millimeters, was 0.36. If heights are measured in inches then the correlation will:
(A) Be unchanged, because correlation does not depend on the units of measurement.
(B) Become zero; for there is no correlation between the two variables.
(C) Decrease, because 1 millimeter is shorter than 1 inch.
(D) Increase, because 1 inch is longer than 1 millimeter.
(E) None of the above.
Question 34. Suppose that 1%of the population has hepatitis. Suppose we have a test
for the disease that has 80% sensitivity and 90% specificity. What is the probability
of a false positive?
(A) .99
(B) .10
(C) .20
(D) .01
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Question 35. The variables x (temperature in ◦ C) and y (temperature in ◦ F) are related
by the formula y = 32 + 1.8x. Therefore the correlation between x and y will be:
(A) 32, because if y = 32 then x = 0.
(B) −1, because if x decreases then y decreases.
(C) 1.8, because if x increases by 1◦ C then y increases by 1.8◦ F.
(D) 0, because if x = 0 then y = 32.
(E) 1, because the variables have a deterministic, linear, increasing relationship.
Question 36. Which of the following is a problem that can occur in a meta-analysis when
data sets are combined inappropriately?
(A) Simpson’s paradox
(B) the vote-counting paradox
(C) the file drawer problem
(D) the Fibonacci effect
Question 37. Lee Salk exposed one group of newly born infants, the treatment group, to
the sound of a human heartbeat. Next, Salk compared their weight gains to those of a
group of newly born infants not exposed, the control group. In Lee Salk’s experiment,
the null hypothesis is:
(A) Infants exposed to the sound of a human heartbeat will hear the heartbeat.
(B) Infants not exposed to the sound of a human heartbeat will hear the heartbeat.
(C) Infants exposed to the sound of a human heartbeat will gain a higher mean weight
than infants who are not exposed to the sound of a heartbeat.
(D) Infants exposed to the sound of a human heartbeat will gain the same mean weight
as infants who are not exposed to the sound of a heartbeat.
Question 38. In a study of farmers’ caffeine levels, a random sample of 25 farmers
yielded a sample mean of 22 and a sample standard deviation (S.D.) of 4. Therefore,
the standard error of the mean (SEM) is:
√
(A) 22/ 25
√
(B) 4 × 25
√
(C) 4/ 25
√
(D) 22 × 25
Question 39. In a study of car ownership in Pennsylvania, the variable “Brand of car
owned” is:
(A) A discrete quantitative variable
(B) A nominal categorical variable
(C) A continuous quantitative variable
(D) An ordinal categorical variable
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Question 40. The mean of a large number of sample proportions from equally-sized
random samples will be approximately:
(A) The area below the normal curve and between -1.96 and +1.96.
(B) A proportion of the population which is never sampled.
(C) The square root of: (true proportion) × (1 − true proportion)/(sample size).
(D) The square root of: (true proportion) × (sample size)/(1 − true proportion).
(E) The true proportion of the population.
Question 41. In a random sample of 400 PSU graduates, 64% stated that they prefer
root beer (over birch beer). Therefore, a 90% confidence interval for the proportion
of all PSU graduates who prefer root beer is:
(A) 0.64 ± 1.64 ×
(B) 0.64 ± 2 ×
p
(C) 0.64 ± 2 ×
p
p
.64/400
.64 × .36/400
.64/400
(D) 0.64 ± 1.64 ×
p
.64 × .36/400
Question 42. Suppose the probability that a child lives with his or her mother as the
sole parent is .216, and the probability that a child lives with his or her father as sole
parent is .031. Then the probability that a child either lives with both or with neither
parent is:
(A) 1 − .216 = .784
(B) 1 − .031 = .969
(C) .216 + .031 = .247
(D) 1 − (.216 + .031) = .753
(E) None of the above
Question 43. As measured by the Stanford-Binet test, IQ scores are approximately normally distributed with mean 100 and standard deviation 16. Mensa is an organization
whose members have IQ scores in the top 2%of the population. To be admitted to
Mensa, a person’s Stanford-Binet IQ score is at least:
(A) 100 + (16 × 0.98) = 115.68.
(B) 100 − (16 × 2.05) = 67.20.
(C) 100 + (16 × 2.05) = 132.80.
(D) 100 − (16 × 0.98) = 84.32.
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Question 44. Hypothetical research question, asked of a random sample of students: Do
you own a pet? (Data and related output below.)
Female
Male
All
No Pet
26
17
43
Yes Pet
50
18
68
All
76
35
111
0.40 +
0.87 +
0.25 +
xxxx =
2.08
Chi-sq =
In the debate between the research advocate and the skeptic, who wins in this case involving
the pet question above?
(A) Skeptic
(B) Neither
(C) Research advocate
(D) Both
Question 45. An advertiser of No-Pain aspirin claims it is the pain-killer most preferred
by consumers. This claim was based on a consumer survey in which the choices were:
Lavid, Acinna, No-Pain, and Yellnot. This is an example of:
(A) An easy question.
(B) An open question.
(C) A difficult question.
(D) A closed question.
Question 46. Suppose you are playing a game and you have a 0.3 probability of winning.
Suppose you decide to play repeatedly until you win. The games are independent.
What is the probability that you win on the first or second try?
(A) .60
(B) .30
(C) .64
(D) .51
Question 47. As measured by the Stanford-Binet test, IQ scores are approximately normally distributed with mean 100 and standard deviation 16. Because of the Empirical
Rule (68-95-99.7 Rule), we can conclude that approximately 68% of all IQ scores will
fall between:
(A) 32 and 168.
(B) 84 and 116.
(C) 0 and 200.
(D) 68 and 132.
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Question 48. Suppose a door prize winner is selected at random from all the people
attending an Italian electrical engineering conference. Your roommate believes that
the winner is more likely to be a black-haired male than a male in general. Your
roommate has committed
(A) the gambler’s fallacy.
(B) the anchoring fallacy.
(C) no fallacy at all; it is well-known that men with black hair have more fun.
(D) the conjunction fallacy.
Question 49. For any data set, the largest number in the five-number summary is the:
(A) Third quartile.
(B) Maximum.
(C) Standard deviation.
(D) Outlier.
(E) Interquartile range.
Question 50. In a boxplot (oriented vertically, with the maximum at the top and the
minimum at the bottom), the proportion of the data falling between the top edge and
the bottom edge of the box itself is
(A) 25%
(B) 99.7%
(C) 50%
(D) Impossible to say without more information
(E) 68%
Question 51.
rejected.
If the sample size is large enough, almost any null hypothesis can be
(A) True
(B) False
Question 52. It has been observed that participants in a statistical experiment sometimes
respond positively to a placebo, a substance which has no active ingredients. This
phenomenon is called the:
(A) Placebo effect.
(B) Interacting effect.
(C) Hawthorne effect.
(D) Confounding effect.
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Question 53. An experiment was conducted to see if adding Quaker State motor oil to
Coppertone suntan lotion enhances tanning. A Type 1 error is:
(A) claim QS does not enhance tanning
(B) claim QS enhances tanning
(C) claim QS does not enhance tanning when it does
(D) claim QS enhances tanning when it does not
Question 54. Meta-analysis is
(A) the use of stratified or cluster sampling
(B) a collection of statistical techniques for combining studies
(C) a way to make statistical significance equivalent to practical significance
(D) the computation of a test statistic followed by a decision regarding a null hypothesis
for data presented in the form of a table
Question 55. Lee Salk exposed one group of newly born infants, the treatment group, to
the sound of a human heartbeat. Next, Salk compared their weight gains to those of
a group of newly born infants not exposed, the control group. In Salk’s experiment, a
Type I error occurs if:
(A) Infants exposed to the sound of a human heartbeat actually hear the heartbeat.
(B) The study fails to reject the hypothesis that exposed infants have the same mean
weight gain as unexposed infants when, in fact, this hypothesis is not valid.
(C) Infants not exposed to the sound of a human heartbeat do not hear the heartbeat.
(D) The study rejects the hypothesis that exposed infants have the same mean weight
gain as unexposed infants when, in fact, this hypothesis is valid.
Question 56. All other things remaining constant, which of the following sample proportions will result in the widest confidence interval:
(A) .2
(B) .5
(C) .1
(D) .4
(E) .3
Question 57. In a statistical study, the sample is:
(A) The group of people or objects for which conclusions are to be made.
(B) A subset of people in the United States.
(C) The subset of the population on which the study collects data.
(D) The collection of data in sample surveys.
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Question 58. The “file drawer” problem refers to
(A) a method of selecting a representative sample from a population.
(B) a gambling choice in which the player must choose among three drawers.
(C) the bias resulting from considering only published studies, which are more likely to
contain statistically significant results than those unpublished studies sitting in file
drawers.
(D) the challenge of building quality furniture.
(E) the fact that studies that have been sitting around for many years in file drawers are
out-of-date.
Question 59. As measured by the Stanford-Binet test, IQ scores are approximately
normally distributed with mean 100 and standard deviation 16. A student who scores
108 on the Stanford-Binet test has a standardized score of:
(A) (108 − 100)/16 = 0.50.
(B) Cannot be calculated because we are given insufficient information.
(C) (108 − 16)/100 = 0.92.
√
(D) (108 − 100)/ 100 = 0.80.
Question 60. Joe Palermo interviewed 507 randomly chosen PSU students and found that
59%of the students in his sample like to play chess. Consider the research question
of whether or not a majority of PSU students like to play chess. The test for this
research question is a:
(A) Two-sided test.
(B) One-sided test.
(C) Both a one-sided and two-sided test.
(D) Neither a one-sided nor two-sided test.
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