Stats ch 6

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.

NOT b. just less than 1.96.

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

NOT d. 50 or a. 10

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 101.6? a. -1.19 b. -1.0 c. -0.87 d. 0.93

a. -1.19

Which of these z scores from a single distribution of scores corresponds to the raw score farthest from the mean of the distribution? a. -2.3 b. -1.5 c. 0.8 d. 1.2

a. -2.3

The distribution of means based on a sample size of 45, pulled from a population distribution with a mean of 100 and a standard deviation of 15, would have a standard error of: a. 2.24. b. 3.00. c. 25.82. d. 4.50.

a. 2.24.

If a distribution of scores has a mean of 90 and a standard deviation of 10, then a score of 70 has a z score that is _____ standard deviation(s) _____ the mean. a. 2; below b. 1; above c. 1; below d. 2; above

a. 2; below

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

a. 30

In a normal standard curve, what percentile corresponds to a z score of 1.0? a. 84 b. 68 c. 96 d. 45

a. 84

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

a. 89.48

The formula for calculating the raw score from a z score is: a. X = z(s) + μ. b. X = z(μ)/s. c. z = (s μ)/X. d. z = (X s)/μ.

a. X = z(s) + μ.

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.

a. adding the mean of the population to the product obtained from multiplying the z score and standard deviation.

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.

a. always 0

The z distribution _____ has a mean of _____. a. always; 0 b. sometimes; 0 c. always; 1 d. sometimes; 1

a. always; 0

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

a. distribution of means

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.

a. how far away from the mean a score is in terms of standard deviations.

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

a. means

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.

a. number of scores increases.

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 re-sampled. c. recorded in order to create a distribution of scores. d. balanced across the mean so that extreme scores are controlled.

a. placed back into the population for additional sampling.

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.

a. standard deviation units.

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

a. z score

The symbol for the population mean is: a. μ. b. Σ. c. σ. d. χ.

a. μ.

The symbol for the standard error is: a. σM. b. σS. c. μM. d. μS.

a. σM.

Which score is more extreme: 0.32 or -0.45? a. 0.32 b. -0.45 c. z scores do not allow us to assess this. d. Scores with different signs cannot be compared.

b. -0.45

Findings that are in the most extreme _____ percent are considered significant and worthy of publishing. a. 1 b. 5 c. 10 d. 50

b. 5

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

b. 50; 50

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

b. 99.69

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

b. lower variance

The process of standardization involves the conversion of raw scores to _____ scores. a. linear b. standard c. normal d. nonlinear

b. standard

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

b. the central limit theorem

According to _____, as sample size increases, the distribution of _____ assume 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

b. the central limit theorem; sample means

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.

b. the mean of the distribution of raw scores.

A _____ is a distribution of z scores. a. normal curve b. z distribution c. standard linear distribution d. standardization

b. z distribution

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

c. 0.11

In a normal standard curve, which percentile corresponds to a z score of -1.0? a. 34 b. 68 c. 16 d. 45

c. 16

Adam scored 70 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. 1.5 standard deviation below the mean c. 2 standard deviations above the mean d. 2 standard deviations below the mean

c. 2 standard deviations above the mean

If a distribution of scores has a mean of 55 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

c. 3

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

c. 87.25

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

c. 96

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.

c. The two students cannot be compared because no standardization procedure was used to permit comparisons.

The z distribution _____ has a standard deviation of _____. a. always; 0 b. sometimes; 0 c. always; 1 d. sometimes; 1

c. always; 1

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.

c. compares that to a distribution of mean by calculating a z statistic.

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.

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.

As sample size _____, the spread of distribution of means _____. a. increases; increases b. decreases; stays the same c. increases; decreases d. decreases; decreases

c. increases; decreases

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

c. mean; standard deviation

The _____ curve forms a symmetrical and mathematically defined bell-shaped pattern. a. asymmetric b. unstandardized c. normal d.nonlinear

c. normal

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.

c. population standard deviation.

The z distribution is a normal distribution of _____ scores. a. sample mean b. population mean c. standardized d. raw

c. standardized

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.

c. teachers may have completed tests for students in order to raise performance levels.

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.

c. the difference between a particular score and the population mean.

The z distribution is equivalent to a distribution of _____ scores. a. mean b. linear c. z d. raw

c. z

The formula for calculating a z score is: a. z = (s X)/μ. b. z = (μ X)/s. c. z = (X μ)/s. d. z = (X s)/μ.

c. z = (X μ)/s.

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.

c. z scores.

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.

c. z statistic.

The symbol for the population standard deviation is: a. μ. b. Σ. c. σ. d. χ.

c. σ.

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

d. -1.0

Adam scored 70 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. 1 c. -2 d. 2

d. 2

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

d. 2.0

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

d. 68

What percent of scores fall beyond 3 standard deviations away from the mean? a. more than 10 b. 10 c. 5 d. less than 1

d. less than 1

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

d. second student because she performed better relative to her class

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

d. standard error

The formula for z based on the mean of a sample is: a. z = (M μM)/μS. b. z = (X μM)/μS. c. z = (X μM)/sM. d. z = (M μM)/sM.

d. z = (M μM)/sM.

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.

resulting in a raw score of 21.27

The formula for the standard error is:

σM=σ/√N