Chapter 4
Standardized Scores and the Normal Distribution
Section A
1. The mean of a set of z scores:
*
a) always equals 0
b) always equals 1
c) depends on the number of scores
d) depends on the shape of the distribution
2. The standard deviation of a set of z scores:
*
a) always equals 0
b) always equals 1
c) depends on the number of scores
d) depends on the shape of the distribution
3. Comparing z scores from two different distributions is most meaningful when:
*
a) both distributions have the same mean
b) both distributions have the same standard deviation
c) both distributions have the same shape
d) both distributions have the same number of scores
4. If a distribution of raw scores is positively skewed, the distribution after converting to z
scores will be:
*
a) positively skewed
b) the standard normal distribution
c) negatively skewed
d) less skewed than the original distribution
5. In a standard normal distribution (i.e., a distribution
scores are above 0?
*
a) none of the scores
b) half of the scores
c) all of the scores
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of z-scores), what proportion of the
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d) it depends on the particular distribution
6. Which of the following has the highest z-score?
*
a) an SAT score of 550
b) a T score of 62
c) an IQ score of 112 (σ = 15)
d) a raw score of 80, if μ = 70 and σ = 12
7. SAT and T scores are often preferred to z-scores, because they are not likely to:
*
a) be less than zero
b) have a skewed distribution
c) underestimate the true score
d) overestimate the true score
8. The standard normal distribution:
*
a) extends to -2 on one side and +2 on the other
b) extends to -4 on one side and +4 on the other
c) extends to -10 on one side and +10 on the other
d) extends to infinity on both sides
9. A sampling distribution is:
a) the distribution within any one sample from a population
b) one distribution randomly selected from many possible distributions
c) a distribution in which each of the individuals has been sampled from the same
population
*
d) a distribution of sample statistics, each from a different random sample of the same
population
10. The mean of the sampling distribution of the mean:
*
a) is equal to the sample mean
b) is equal to the population mean
c) is always smaller than the population mean
d) depends on the size of the samples
11. The variance of the sampling distribution of the mean:
a) is equal to the population mean
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b) is equal to the population variance
c) is never larger than the population variance
d) depends on the number of samples in the sampling distribution
*
12. The standard error of the mean will be approximately equal to:
*
a) the standard deviation of many sample means
b) the mean of many sample standard deviations
c) the mean of many sample means
d) the standard deviation of many sample standard deviations
Section B
13. If height is measured in meters, and your friend has a
z-score of +.2, what will your friend's z-score be if all the heights (including your friend's) are
multiplied by 100 to convert to centimeters?
a) +20 b) +.2 c) +2 d) +200
-14. You receive the results of your practice GRE's and find that your math score is 700. If the
mean of the raw scores is 34, with a standard deviation of 6, what is your raw score for that test?
a) 36 b) 40 c) 42 d) 46
-15. If the mean for a statistics quiz is 8, with a standard deviation of 2, what raw score
corresponds to a z-score of -1.5?
a) 5 b) 6.5 c) 9.5 d) 11
-16. On a scale of depression, a particular patient's T score
is 27. What is that patient's z-score?
a) -2.7 b) -2.3 c) +2.3 d) +2.7
-17. On the Wechsler IQ test (μ = 100, σ = 15), approximately what proportion of the population
can be expected to score above 120?
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a) .408 b) .341 c) .159 d) .092
-18. What is the approximate percentile rank of someone who scored a 105 on the Wechsler IQ
test (σ = 15)?
a) 37 b) 63 c) 83 d) 87
-19. If resting heart rate is normally distributed in the population with μ = 72 and σ = 8, what is
the percentile rank (approximately) of someone whose resting heart rate is 62?
a) .11 b) .40 c) .61 d) .89
-20. To join a particular volunteer fire department you must be at least as tall as 75% of the
population (i.e., at the 75th percentile or higher). Assuming that the average height of all people
is 67.5 inches, with a standard deviation of 3 inches, how tall must you be (in inches)?
a) 68.5 b) 69.5 c) 70.5 d) 71.5
-21. Assuming that the mean annual income in the United States is $24,000 a year with a
standard deviation of $5000. What range of (approximate) incomes encompass the middle 90%
of the country?
a) $19,000 to $29,000
b) $16,500 to $31,500
* c) $15,775 to $32,225
d) $14,200 to $33,800
22. If the population distribution is positively skewed, which of the following will be true about
the shape of the sampling distribution of the mean for a sample size of 10?
*
a) It will be the same as the population distribution.
b) It will be less positively skewed than the population distribution.
c) It will be negatively skewed.
d) It will be the same as the normal distribution.
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23. Assume that the mean number of times Americans exercise per week is equal to 2, with a
standard deviation of .55. What is the standard error of the mean for sample sizes of 30?
a) .02 b) .10 c) .37 d) 3.64
-24. In order for the standard error of the mean to equal 1.5 when the sample size is 9, what must
be the value of the standard deviation of the population?
a) .5 b) 1.5 c) 4.5 d) 13.5
-25. If the mean weight for all men is 160 pounds with a standard deviation of 20 pounds, and
you want the standard deviation of the sampling distribution of the mean to be only one pound,
how large would the samples have to be?
a) 20 b) 40 c) 160 d) 400
-26. Heart rates for a group of 25 joggers were measured, and the mean of the group was found to
be 65 bpm. If the mean of the population is 72 bpm with a standard deviation of 10, what is the
z-score for this group compared to other groups of the same size?
a) .7 b) 3.5 c) 7.0 d) 17.5
-27. A class of 40 students is found to have a mean math SAT score of 570. Assuming μ = 500
and σ = 100, what is the z-score for this group compared to other groups of the same size?
a) .7 b) 1.4 c) 3.5 d) 4.4
-28. In doing some research at the library, you find out that the average reading speed is 2.5
words per second with a standard deviation of .5. What is the probability of randomly selecting
a group of 20 subjects whose average reading speed is faster than 2.6 words per second?
a) .16 b) .19 c) .42 d) .46
-29. The z-score for the height of a group of men is -1.33 with respect to other groups the same
size. If the mean height for the group is 68 inches and the mean for the population of men is 69
inches with a standard deviation of 3, what is the size of the group?
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a) 16 b) 32 c) 48 d) 64
-30. Assuming that for IQ μ = 100 and σ = 15, what is the probability of randomly selecting a
group of 100 people whose mean IQ is between 100 and 102?
a) .09 b) .15 c) .33 d) .41
--
Section C
31. The Central Limit Theorem applies only when:
*
a) the size of the samples is infinite
b) the variance of the population distribution is infinite
c) the shape of the population distribution is normal
d) each selection in a sample is independent of all other selections
32. Which of the following conditions requires that rather large sample sizes must be used
before the sampling distribution resembles the normal distribution?
*
a) a strongly skewed population distribution
b) a very large population variance
c) a small, finite population
d) all of the above
33. Which of the following characteristics of psychological research poses the most severe
problem in assuming that the Central Limit Theorem applies to the sampling distribution?
a) sampling without replacement
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b) the use of variables that are not normally distributed
c) the use of convenient rather than random samples
d) the fact that only a few samples are drawn in any one study
34. Strictly speaking, successive selections from a population can only be truly random when
sampling:
*
a) exhaustively
b) conditionally
c) with replacement
d) without replacement
35. What is the approximate probability that a randomly selected student will have a verbal SAT
score that is either above 600 or below 400?
a) .16 b) .32 c) .34 d) .68
--
36. What is the approximate probability of picking someone at random who has a Wechsler IQ
(σ = 15) between 85 and 130?
a) .34 b) .48 c) .82 d) .98
-37. If two events that are mutually exclusive have probabilities of .2 and .5, respectively, what
is the likelihood that either one or the other will occur?
a) .01 b) .1 c) .3 d) .7
-38. If two events each have a probability of .4 and the probability of both events occurring is
.16, the events must be:
*
a) independent
b) mutually exclusive
c) complementary
d) unconditional
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39. If two events each have a probability of .6, the events cannot be:
*
a) independent
b) mutually exclusive
c) exhaustive
d) overlapping
40. Suppose that there are five women and three men on the student association steering
committee. If two members are to be selected at random to co-lead the committee, what is the
probability that both will be men (assuming sampling without replacement)?
a) 6/64 b) 9/64 c) 6/56 d) 9/56
--
Chapter 5
Introduction to Hypothesis Testing: The One-Sample z Test
Section A
1. Suppose that the variable you have measured in a sample of subjects does not have a normal
distribution in the population. Which of the following is recommended?
a) convert all the measurements to z-scores
b) eliminate as many measurements as necessary until your sample distribution looks like the
normal distribution
* c) use a fairly large sample size (at least 30 or 40)
d) choose another variable to measure -- only a normally distributed variable will give you
valid results
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2. Suppose you are testing the idea that people with brown eyes have a greater pain tolerance
than people with blue eyes. Which would be an appropriate null hypothesis?
a) The mean for the sample of brown-eyed people will be the same as the mean for the blueeyed sample.
b) The mean for the sample of brown-eyed people will be greater than the mean for the blueeyed sample.
* c) The population mean for the brown-eyed people will be the same as the population mean
for the blue-eyed people.
d) The population mean for the brown-eyed people will be greater than the population mean
for the blue-eyed people
3. When the null hypothesis is actually true:
*
a) the experimental results will not come out statistically significant
b) it is not possible to make a Type I error
c) significant results can be attributed to chance factors
d) the p level will be the same as the alpha level
4. The main advantage of a one-tailed test, compared to a two-tailed test is that:
*
a) only half the calculation is required
b) only half of the calculated t value is required
c) there is only half the risk of a Type I error
d) a smaller critical value must be exceeded
5. As the calculated z-score for a one-sample test gets larger:
*
a) p gets larger
b) p gets smaller
c) p remains the same, but alpha gets larger
d) p remains the same, but alpha gets smaller
6. If you find a p value to be 1.1, you can be sure that:
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a) the null hypothesis will be rejected
b) the null hypothesis will be accepted
c) an error in calculation has been made
d) a two-tailed test has been conducted
7. If you find a p value to be .5, and alpha = .05, what can you conclude about your experiment?
*
a) There is little chance of making a Type II error.
b) A calculation error has been made.
c) The null hypothesis can be rejected.
d) The null hypothesis cannot be rejected.
8. The easiest way to reduce Type I errors is to:
*
a) make your p value smaller
b) make your p value larger
c) make your alpha level smaller
d) make your alpha level larger
9. Compared to Type II errors, Type I errors:
*
a) are more directly controlled by null hypothesis testing
b) are more difficult to detect
c) are more likely to lead to the abandonment of a line of research
d) are far more common in psychological research
10. The main purpose of null hypothesis testing is to:
*
a) control Type I errors
b) control Type II errors
c) control the number of null hypotheses
d) prove the existence of null hypotheses
Section B
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11. If alpha were set to .02 for a two-tailed test, what would be the critical values for z?
a) ±1.75 b) ±2.05 c) ±2.33 d) ±2.58
-12. If you were always to perform a two-tailed test using ±1.75 as your critical values for z,
what would your Type I error rate be?
a) .01 b) .02 c) .04 d) .08
-13. If a one-sample experiment results in a two-tailed p value of .3, what must the z-score have
been (approximately)?
a) .52 b) 1.04 c) 1.88 d) 2.17
-14. A group of 16 girls training for the Olympics is found to have an average body fat
percentage that is half of a standard deviation below the population mean for girls the same age.
What is the z-score for this group (as compared to other groups the same size)?
a) .5
*
b) 2.0
c) 4.0
d) cannot be determined without further information
15. A researcher tests a random sample of 25 college students to see how many hours they spend
each day at the computer. The sample mean is 1.25 hours. If the population mean for this
variable is .75 hours with a standard deviation of .4, what is the z-score for this group of college
students (as compared to other groups the same size)?
a) 1.25 b) 2.5 c) 5.0 d) 6.25
-16. Suppose that a group of 50 regular "fast-food" consumers has a mean systolic blood pressure
of 122 mm Hg. If the population mean is 120 mm Hg. with a standard deviation of 10, what is
the two-tailed p level that corresponds to the z-score for this group (as compared to other groups
the same size)?
a) .24 b) .16 c) .12 d) .08
--
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17. If a sample of students before an exam has a mean heart rate of 74 bpm, and the population
mean is 72 bpm, with a standard deviation of 8, how many subjects must be in the sample to
attain a calculated z-score of 2.0?
a) 4 b) 8 c) 16 d) 64
-18. The IQ (μ = 100, σ = 15) scores for an advanced class at an elementary school are as
follows: 102, 104, 100, 107, 105, 111, 101, 114, 110. What is the z-score for this group (as
compared to other groups the same size)?
a) 1.2 b) 2.4 c) 3.6 d) 4.8
-19. The birth weights (in pounds) for a group of infants whose mothers were fed a special diet
during pregnancy are as follows: 8.6, 7.6, 7.5, 8.1, 7.0, 7.4, 8.3, 8.0, 8.7, 7.8, 7.1, 7.5. If the
average birth weight of all infants is 7.2 pounds with a standard deviation of 1.2 pounds, what is
the one-tailed p value that corresponds to the z-score for this group of infants?
a) .042 b) .084 c) .168 d) .336
-20. A review course designed to improve the verbal SAT scores
(μ = 500, σ = 100) of its participants just found that the average verbal SAT score for its last
group of graduates is 510. How large would the class have to be for this group to be
significantly different from the population at the .05 level, two-tailed?
a) 20 b) 200 c) 385 d) 400
--
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Section C
21. In what percentage (approximately) of psychology experiments is the null hypothesis
actually true?
*
a) none
b) 5%
c) it depends on the actual alpha levels being used
d) there is no way to estimate this
22. If we know that the null hypothesis was true for 30 experiments conducted at a particular
laboratory last year, about how many Type I errors would be expected among that group of
studies?
*
a) none
b) 30
c) it depends on the actual alpha levels being used
d) there is no way to estimate this
23. If a large research institute is planning to conduct 80 studies next year, testing each at the .05
level, what can be expected for the total number of Type I errors during that time period?
*
a) zero
b) about 4
c) anywhere between zero and about 4
d) there is no way to estimate this
24. Of all the studies conducted by a large research institute over the last five years, 80 studies
were statistically significant at the .05 level. What can be expected for the total number of Type
II errors among those 80 results?
*
a) zero
b) about 4
c) anywhere between zero and about 4
d) there is no way to estimate this
25. Which of the following conditions that exist in psychological research tends to increase the
percentage of published results that are actually Type I errors?
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*
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a) fallacies concerning conditional probabilities
b) the use of alphas less than .05
c) the "file-drawer" problem
d) the wide-spread use of powerful treatments
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Chapter 6
Interval Estimation and the t Distribution
Section A
1. A t-test is used in place of the z-score for groups, when which of the following must
be estimated?
*
a) the sample mean
b) the population mean
c) the sample standard deviation
d) the population standard deviation
2. You need to use the t distribution as your null hypothesis distribution whenever:
*
a) the population mean and variance are unknown
b) the population mean is unknown and the sample size is small
c) the population variance is small and the sample size is unknown
d) the population variance is unknown and the sample size is small
3. The t distribution that you use to find your critical values closely resembles the normal
distribution when:
*
a) the sample mean is large
b) the sample variance is large
c) the sample size is large
d) the population standard deviation is large
4. If the sample size for a one-group experiment increases but the calculated t value
remains the same, which of the following occurs?
*
a) the p level decreases
b) the p level remains the same
c) the p level increases
d) the chance of making a Type I error decreases
5. The critical t value for a one-group experiment will never be:
a) less than zero
b) less than 2
*
c) smaller than the corresponding critical z
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d) larger than the corresponding critical z
6. Of all the 95% confidence intervals for the population mean that you construct, about
what percent will contain the true population mean?
*
a) about 5%
b) about 95%
c) 100%
d) it depends on the sample sizes that were used
7. Of all the 95% confidence intervals for the population mean that you construct, about
what percent will contain the sample mean?
*
a) about 5%
b) about 95%
c) 100%
d) it depends on the sample sizes that were used
8. The critical t values that are used to find a confidence interval for the population mean
will get larger if:
*
a) the sample size becomes smaller
b) the level of confidence is made smaller
c) the standard deviation becomes smaller
d) the population mean becomes larger
9. The best point estimate for the population mean is:
*
a) the sample mean
b) the sample mean divided by the sample size
c) the sample mean divided by the degrees of freedom
d) the sample mean divided by the unbiased sample standard deviation
10. The smallest that the width of a 95% confidence interval can get is:
a) determined by the sample standard deviation
b) determined by the critical values for a .05, two-tailed test
c) two times 1.96 = 3.92
* d) not limited; it can always be made smaller by increasing N
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11. If a 95% confidence interval for the population mean ranges from 22 to 28, which of
the following can be concluded?
* a) The null hypothesis that the population mean equals 28.1 can be rejected at the .05
level, two-tailed.
b) The null hypothesis that the population mean equals 28.1 can be rejected at the .01
level, two-tailed.
c) The null hypothesis that the population mean equals 28.1 cannot be rejected at the
.05 level, two-tailed.
d) None of the above can be concluded without further information.
12. Every point contained in a 95% confidence interval for the population mean is:
a) contained in the 90% CI based on the same data
* b) contained in the 99% CI based on the same data
c) significantly different from the population mean at the .05 level, two-tailed
d) significantly different from the sample mean at the .05 level, two-tailed
Section B
13. If a one-sample t-test involves 14 subjects, what is the critical t value for a .01, onetailed test?
a) 2.624 b) 2.650 c) 2.977 d) 3.012
-14. A group of 36 ulcer patients is found to have a mean score of 45 and a standard
deviation of 12 on a measure of repressed anger. What is the t value if this sample is
being compared to a population whose mean is 42.5?
a) 1.25 b) 2.5 c) 5.0 d) 7.5
-15. Thirty schizophrenics score a mean of 12, with a standard deviation of 3.5 on a shortterm memory test. If the mean for the general population is 13.7, what is the two-tailed p
corresponding to the one-sample t value comparing the 30 schizophrenics to the general
population?
a) > .05
b) between .05 and .02
* c) between .02 and .01
d) < .01
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16. A researcher wants to know if drinking affects driving performance. Driving is
simulated with a video game. Extensive testing has established that the population mean
for completing one lap in the game is 30 seconds in the sober state. After consuming four
ounces of alcohol, a sample of 20 subjects scores a mean of 34 seconds, with a standard
deviation of 10 seconds. What is the one-tailed p value associated with the t value for
this experiment?
a) > .05
* b) between .05 and .025
c) between .025 and .01
d) < .01
17. A group of students who agreed not to watch television for six months is asked how
many books (other than those required for school) each read during that time period. The
data are as follows: 7, 3, 8, 1, 2, 8, 4, 3, 0, 5. If the population mean for the number of
nonrequired books read in six months by students the same age is 2.0, what is the t value
for this group?
a) .74 b) 1.44 c) 2.33 d) 4.56
-18. You are told that a particular 95% confidence interval for the population mean ranges
from 45.32 to 76.68. What is the value of the sample mean upon which this interval is
based?
a) 45.32
* b) 61
c) 132
d) cannot be determined without further information
19. The marketing department of a manufacturing company wanted to find out how
many blank video cassettes are purchased by the average American each year. The data
for a random sample of Americans are as follows: 7, 0, 6, 3, 10, 0, 4, 9, 6, 3, 12, 0, 5, 1,
8, 6. What are the limits of the 99% confidence interval for the mean of the population?
*
a) 2.27 - 7.73
b) 3.03 - 6.97
c) 1.29 - 8.71
d) 2.59 - 7.41
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20. Suppose that the mean number of blank video cassettes purchased in Japan each year
is known to be 7.2 per person. Referring to the data in the previous question, what is the t
value for determining whether Americans differ significantly from the Japanese in blank
video cassette consumption?
a) 2.16 b) 2.20 c) 2.37 d) 9.50
-Section C
21. The sampling distribution of the variance, when N is small, is:
*
a) positively skewed
b) negatively skewed
c) indistinguishable from the normal distribution
d) not smooth or continuous
22. If the mean of a sampling distribution for a particular statistic differs from the
population parameter that the statistic is an estimate of, that statistic is said to be:
a) an inconsistent estimator
b) a relatively inefficient estimator
c) a biased estimator
d) an unreliable estimator
*
23. Which of the following happens to the sampling distribution of the variance as the
sample size increases?
a) it becomes more skewed
b) it become more like the normal distribution
c) it becomes more like the chi-square distribution
d) it becomes smoother and more continuous
*
24. If the variance of 18 participants in an experiment is being compared to the
population variance with a chi-square test, what is the critical value of chi-square for a
.05 test?
a) 24.77
b) 27.59
--
c) 28.87
d) 30.19
25. A teacher obtains the IQ scores for the 30 students in her class, and finds the standard
deviation to be 20. If the standard deviation for the IQ test is 15, what is the value of the
chi-square statistic for testing whether this class is a random sample from the population?
a) 51.56
b) 53.33
c) 16.31
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19
d) 38.67