Deck 6: The Normal Curve, Standardization and Z Scores

Question 1

Gibson (1986) asked a sample of college students to complete a self-esteem scale on which the midpoint of the scale was the score 108.He found that the average self-esteem score for this sample was 135.2, well above the actual midpoint of the scale.Given that the standard deviation of self-esteem scores was 28.15, what would be the z score for a person whose self-esteem score was 104.28?

A) -1.10
B) -0.85
C) 0.85
D) 1.10

Answer 1

-1.10

Question 2

A _____ represents the number of standard deviations a particular score is from the mean average.

A) z score
B) standard mean
C) standardization score
D) skewed score

Answer 2

z score

Question 3

If a distribution of scores has a mean of 50 and a standard deviation of 5, then a score of 70 has a z score that is _____ standard deviation(s) from the mean.

A) 1
B) 2
C) 3
D) 4

Answer 3

4

Question 4

On the first statistics exam, the class average was 70 with a standard deviation of 6.Adam scored 82.What is his z score?

A) -1.0
B) -2.0
C) 6.0
D) 2.0

Question 5

The _____ curve forms a symmetrical and mathematically defined bell-shaped pattern.

A) asymmetric
B) unstandardized
C) normal
D) nonlinear

Question 6

The process of standardization involves the conversion of raw scores to _____ scores.

A) linear
B) standard
C) normal
D) nonlinear

Question 7

The mean of the distribution of a set of z scores is:

A) always 0.
B) always 1.
C) the same as the mean of the distribution of raw scores.
D) the score corresponding to the 50th percentile in the raw score distribution.

Question 8

Which of these z scores from a single distribution of scores corresponds to the raw score farthest from the mean of the distribution?

A) -1.4
B) -05
C) 0.2
D) 1.6

Question 9

To compare two scores that are measured on different scales, one needs to transform the scores into:

A) standard deviations.
B) means.
C) z scores.
D) population parameters.

Question 10

Jenna scored 40 on a standardized test of reading ability where the mean score is 50 and the standard deviation is 10.Based on this information, what is Jenna's z score?

A) -2.0
B) 2.0
C) 1.0
D) -1.0

Question 11

A z score is a measure of:

A) how far away from the mean a score is in terms of standard deviations.
B) how far away from the mean a score is in terms of inches.
C) the strength of the relationship between two variables.
D) the strength of the relationship between a score and its mean.

Question 12

A person with a z score of 0 would have a raw score equal to:

A) the lowest score in the distribution of raw scores.
B) the mean of the distribution of raw scores.
C) the highest score in the distribution of raw scores.
D) 0.

Question 13

If a distribution of scores has a mean of 60 and a standard deviation of 10, then a score of 50 has a z score that is _____ standard deviation(s) _____ the mean.

A) 2; below
B) 1; above
C) 1; below
D) 2; above

Question 14

Two students from two different schools recently took a science test.The first student correctly answered 34 questions and the second student correctly answered 48 questions.What can be concluded from the two students' test scores?

A) The second student is smarter than the first student.
B) The two students did equally well on the exam.
C) The two students cannot be compared because no standardization procedure was used to permit comparisons.
D) The two students cannot be compared because the scores did not form a linear curve.

Question 15

Distributions of scores approach the normal distribution as the:

A) number of scores increases.
B) number of scores decreases.
C) variance increases.
D) variance decreases.

Question 16

The z distribution _____ has a standard deviation of _____.

A) always; 0
B) sometimes; 0
C) always; 1
D) sometimes; 1

Question 17

Any raw score can be converted into a z score as long as you know the _____ and _____ of the distribution.

A) median; mean
B) median; standard deviation
C) mean; standard deviation
D) mean; range

Question 18

Adam scored 60 on his final exam.His class's average score was 50, with a standard deviation of 10.How many standard deviations is Adam's score from the mean?

A) 1 standard deviation above the mean
B) 1 standard deviation below the mean
C) 2 standard deviations above the mean
D) 2 standard deviations below the mean

Question 19

The z distribution _____ has a mean of _____.

A) always; 0
B) sometimes; 0
C) always; 1
D) sometimes; 1

Question 20

Adam scored 45 on his final exam.His class's average score was 50, with a standard deviation of 10.What is Adam's z score?

A) -1
B) -0.5
C) 0.5
D) 1.5

Question 21

The formula for calculating the raw score from a z score is:

A) X = z(s) + $\mu$ .
B) X = z( $\mu$ )/ s.
C) z = (s - $\mu$ )/X.
D) z = (X - s)/ $\mu$ .

Question 22

The symbol for the population standard deviation is:

A) $\mu$ .
B) X.
C) z.
D) s.

Question 23

The first step in converting a z score into a raw score is multiplying the z score by the:

A) population standard less the population mean.
B) the raw score.
C) population standard deviation.
D) population mean.

Question 24

According to the 2012-2013 annual report of the American Psychological Association's survey of faculty salaries in graduate departments of psychology, the average salary for a new (less than 3 years) full professor was $92,000 with a standard deviation of $32,845.What is the z score of a new full professor making $95,500?

A) -0.62
B) -0.11
C) 0.11
D) 0.62

Question 25

The mean for the population is 67 with a standard deviation of 8.78.Given a z score of 2.56, what is the raw score?

A) 89.48
B) 75.78
C) 87.88
D) 69.56

Question 26

Two students recently took algebra class tests.The students are at different schools but wanted to compare their performance.The first student scored 80 on the test.Her class average was 90 with a standard deviation of 10.The second student scored 70.Her class average was 50 with a standard deviation of 10.Which student did better?

A) first student because she had a higher score
B) second student because she had an average score
C) first student because she performed better relative to her class
D) second student because she performed better relative to her class

Question 27

Which score is more extreme: 0.68 or -0.92?

A) 0.68
B) -0.92
C) z scores do not allow us to assess this.
D) Scores with different signs cannot be compared.

Question 28

A _____ is a distribution of z scores.

A) normal curve
B) z distribution
C) standard linear distribution
D) standardization

Question 29

The z distribution always has a standard deviation of _____.

A) 0
B) 0.5
C) 1
D) 10

Question 30

Daniel wanted to know his approximate score on the final exam for his mathematics class.His professor hinted that his score was well above the class average.The professor announced that the mean for the class final exam was 88 with a standard deviation of 7.Given Daniel's z score of 1.67, what is the raw score for his exam grade?

A) 100.00
B) 99.69
C) 102.45
D) 88.17

Question 31

The formula for calculating a z score is:

A) z = (s - X)/ $\mu$ .
B) z = ( $\mu$ - X)/ s.
C) z = (X - $\mu$ )/s.
D) z = (X - s)/ $\mu$ .

Question 32

The second step in calculating a z score is expressing the obtained values in:

A) standard deviation units.
B) linear form.
C) nonlinear form.
D) distribution of means.

Question 33

z scores are useful because they:

A) allow us to convert raw scores to mean scores, compare scores from different samples, and transform populations into samples.
B) transform linear scores into nonlinear scores, convert nonlinear scores back into linear scores, and allow us to obtain comparisons between nonlinear and linear scores.
C) give us an understanding of where a score falls in relation to the mean of its underlying population, allow comparisons to be made between scores from different distributions, and permit the transformation of z scores into percentiles.
D) reduce the probability of Type I and Type II errors, allow us to compare raw scores with standard scores, and permit the transformation of raw scores into percentiles.

Question 34

The z distribution always has a mean of _____.

A) 0
B) 0.5
C) 1
D) 10

Question 35

The z distribution is equivalent to a distribution of _____ scores.

A) mean
B) linear
C) z
D) raw

Question 36

The z distribution is a normal distribution of _____ scores.

A) sample mean
B) population mean
C) standardized
D) raw

Question 37

The mean for the population is 80 with a standard deviation of 5.Given a z score of 1.45, what is the raw score?

A) 88.00
B) 90.00
C) 87.25
D) 1.00

Question 38

The symbol for the population mean is:

A) $\mu$ .
B) X.
C) z.
D) s.

Question 39

The second step in converting a z score into a raw score is:

A) adding the mean of the population to the product obtained from multiplying the z score and standard deviation.
B) subtracting the mean of the population from the product obtained by multiplying the z score and standard deviation.
C) dividing the mean of the population into the product obtained by multiplying the z score and standard deviation.
D) multiplying the mean of the population and the product obtained from multiplying the z score and standard deviation.

Question 40

The first step in calculating a z score is calculating:

A) a standard deviation score.
B) the raw scores and subtracting from the mean of the sample.
C) the difference between a particular score and the population mean.
D) the difference between a particular score and the sample mean.

Question 41

In a normal standard curve, approximately _____ percent of scores fall within 2 standard deviations from the mean

A) 34
B) 48
C) 96
D) 68

Question 42

According to _____, as sample size increases, the distribution of _____ assumes a normal curve.

A) the standardized distribution; sample scores
B) the central limit theorem; sample means
C) the z-score distribution; population scores
D) hypothesis testing; raw scores

Question 43

The formula for the standard error is:

A) $\sigma _ { M } = \sigma / \sqrt { N }$
B) $\sigma _ { S } = \mu / \sqrt { N }$
C) $\sigma _ { M } = \sum / N$
D) $\sigma _ { S } = \sum / ( N - 1 )$

Question 44

Given the properties of the standard normal curve, we know that _____ percent of all scores fall below the mean and _____ percent fall above the mean.

A) 68; 68
B) 50; 50
C) 34; 34
D) 48; 48

Question 45

As sample size _____, the spread of distribution of means _____.

A) increases; increases
B) decreases; stays the same
C) increases; decreases
D) decreases; decreases

Question 46

A distribution of means would be more likely to have a(n) _____ compared to a distribution of raw scores.

A) higher variance
B) lower variance
C) higher standard deviation
D) equal standard deviation

Question 47

What percent of scores fall beyond 2 standard deviations away from the mean?

A) 28
B) 14
C) 4
D) 2

Question 48

Because of _____, skewed distributions approximate normal curves when means are based on larger samples.

A) kurtosis
B) the central limit theorem
C) hypothesis testing
D) z scores

Question 49

In a normal standard curve, approximately _____ percent of scores fall within 1 standard deviation from the mean.

A) 34
B) 46
C) 96
D) 68

Question 50

A _____ is composed of means based on samples rather than raw scores.

A) distribution of means
B) distribution of z scores
C) standardized distribution
D) percentile distribution

Question 51

The symbol for the standard error is:

A) s_M.
B) s_S.
C) $\mu$ _M.
D) $\mu$ _S.

Question 52

If samples have at least _____ scores, the distribution of means will most likely approximate a normal curve.

A) 30
B) 50
C) 88
D) 100

Question 53

The term _____ is used for the distribution of means in place of the term standard deviation.

A) standard variance
B) population variance
C) mean variance
D) standard error

Question 54

When creating a distribution of means, it is important that whatever scores are sampled to compute the means are:

A) placed back into the population for additional sampling.
B) separated out from the population so that they cannot be resampled.
C) recorded in order to create a distribution of scores.
D) balanced across the mean so that extreme scores are controlled.

Question 55

A distribution of scores has a mean of 20.2 with a standard deviation of 0.89.Compare a score of 21.26 with a z score of 1.2.Which statement is correct?

A) The score of 21.26 is greater.
B) The z score of 1.2 is greater, resulting in a raw score of 21.27.
C) The z score of 1.2 is lower, resulting in a raw score of 21.4.
D) The z score of 1.2 is greater, resulting in a raw score of 22.19.

Question 56

Sample means based on at least _____ scores tend to approximate a normal distribution, even when the underlying population is skewed.

A) 10
B) 25
C) 30
D) 50

Question 57

In a normal standard curve, which percentile corresponds to a z score of -1.0?

A) 34
B) 68
C) 16
D) 45

Question 58

Repeated sampling of _____ approximates a normal curve, even when the underlying population is skewed.

A) means
B) standard deviations
C) variance estimates
D) population parameters

Question 59

The distribution of means based on a sample size of 20, pulled from a population distribution with a mean of 100 and a standard deviation of 15, would have a standard error of:

A) 1.33.
B) 3.35.
C) 5.16.
D) 5.33.

Question 60

In a normal standard curve, what percentile corresponds to a z score of 1.0?

A) 84
B) 68
C) 96
D) 45

Question 61

Standard scores represent the number of standard deviations a particular score is from the median.

Question 62

Irregular patterns of correct answers shared by multiple students on standardized tests have led to speculation that:

A) standardized tests are prone to errors.
B) students often cheat on tests by copying from each other.
C) teachers may have completed tests for students in order to raise performance levels.
D) researchers are motivated to alter data to reach statistical significance.

Question 63

Any raw score can be converted into a z score as long as you know the median and standard deviation of the distribution.

Question 64

As sample size _____, the mean of a distribution of means _____.

A) increases; increases
B) increases; stays the same
C) increases; decreases
D) decreases; increases

Question 65

Findings that are in the most extreme _____ percent are considered significant and worthy of publishing.

A) 1
B) 5
C) 10
D) 50

Question 66

Gerber and Malhotra (2006) found an irregularly high spike in published z scores:

A) just greater than 1.96.
B) just less than 1.96.
C) around 1.00.
D) out as far as 9.16.

Question 67

Any raw score can be converted into a z score as long as you know the mean and median of the distribution.

Question 68

A negative z score will convert into a raw score that is above the mean of its distribution.

Question 69

A positive z score will convert into a raw score that is below the mean of its distribution.

Question 70

Since one rarely has access to an entire population, one typically calculates the mean of a sample and:

A) compares that to the z distribution.
B) computes a standardized score for that mean.
C) compares that to a distribution of mean by calculating a z statistic.
D) standardizes that using information about the center and spread of the population of scores.

Question 71

The formula for z based on the mean of a sample is:

A) z = (M - $\mu$ _M)/ $\mu$ _s.
B) z = (X - $\mu$ _M)/ $\mu$ _s.
C) z = (X - $\mu$ _M)/ s_M.
D) z = (M - $\mu$ _M)/s_M.

Question 72

A z score is the distance a score is from the mean of its distribution, expressed in standard deviations.

Question 73

The mean of the z distribution is 0.

Question 74

If you have a z score of 0, then you have a raw score equal to the mean.

Question 75

The standard deviation of the z distribution is 0.

Question 76

A z score is the distance a score is from the mean of its distribution, expressed in variance.

Question 77

The mean of the z distribution is 1.0.

Question 78

Data approaches a normal distribution as sample size increases, thus making sample size important in relation to the normal curve.

Question 79

The standard deviation of the z distribution is 1.0.

Question 80

When calculating a z score for a distribution of means, the z score is referred to as a:

A) standard score.
B) standardized score.
C) z statistic.
D) central limit theorem.