Stat Quiz 6

Which score is more extreme: 0.78 or -0.93?

-0.93

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?

-1.10

A person who scored exactly at the mean of the distribution of raw scores would have a z score of _______.

0

The z distribution always has a mean of _____.

0

According to the 2015 annual report of the American Psychological Association's on salaries in psychology. The average salary for those working in a teaching position was $71,471, with a standard deviation of $24,703. What is the z score of a professor making $85,500?

0.57

The z distribution always has a standard deviation of _____.

1

Tej scored 60 on his final exam. His class's average score was 55, with a standard deviation of 5. How many standard deviations is Tej's score from the mean?

1 standard deviation above the mean

Approximately 68 percent of scores fall within _______ standard deviation(s) of the mean.

1, one

A z score of -2.0 is equivalent to the _______ percentile.

2nd

Distributions of means computed from samples of at least _______ observations usually produce an approximately normal curve.

30

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

30

In the z distribution, _______ percent of scores fall between the mean and a z score of 1.0, or the mean and a z score of -1.0.

34

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

4

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

5

In the z distribution, _______ percent of scores fall above the mean.

50

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.

50; 50

A z score of 0 is equivalent to the _______ percentile.

50th

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

68

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

84

A z score of +1.0 is equivalent to the _______ percentile.

84th

The mean for the population is 82 with a standard deviation of 6. Given a z score of 1.45, what is the raw score?

90.70

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

96

A z score of +2.0 is equivalent to the _______ percentile.

98th

Mason wanted to know his approximate score on the final exam for his statistics 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 Mason's z score of 1.67, what is the raw score for his exam grade?

99.69

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

False

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

False

A z score allows assessment of the percentile of a raw score, but an equivalent assessment of a sample mean cannot be made.

False

A z score allows one to compare scores to each other, but not when they are based on different scales.

False

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

False

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

False

If a score has a z score of 1, then the raw score equals to the mean.

False

In a distribution with a mean of 150 and a standard deviation of 20, a z score of -1.0 would convert into a raw score of 120.

False

Less than 5 percent of the distribution of scores falls beyond a z score of +/-1.0.

False

Standard error is the variance of a distribution of means.

False

Standard error is the variance of a distribution of means. Correct Answer

False

The percentage of area under the curve for a negative z score will be negative.

False

The standard deviation of the z distribution is 0.

False

When attempting to create a distribution of means, we sample with replacement; that is, we do not put data back in the sample after we have computed the mean of those data.

False

When comparing two z scores to assess performance on an exam, one would conclude that a student with a z of -2.3 outperformed someone with a z of 1.7 because the first score is more extreme.

False

Two students from two different high schools recently took a math test. The first student correctly answered 37 questions and the second student correctly answered 45 questions. What can be concluded from the two students' test scores?

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

A distribution of scores has a mean of 20.4 with a standard deviation of 0.89. Compare a score of 21.26 with a z score of 1.2. Which statement is correct?

The z score of 1.2 is greater, resulting in a raw score of 21.47.

A distribution of means comprises many, many means of samples, all of the same size.

True

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

True

A z score allows one to compare scores to each other, even when they are based on different scales.

True

A z score computed for a sample mean is called a z statistic.

True

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

True

A z statistic is used to refer to a distribution of means.

True

At a z score of 0, your score is at the 50th percentile.

True

Because a z score is the number of standard deviations a score is from its mean, the first step in converting a z score back to a raw score is multiplying z and the standard deviation.

True

Data drawn from a normally distributed population approaches a normal distribution as sample size increases, thus making sample size important in relation to the normal curve.

True

Even when the distribution of scores in the population is not normal, the sampling distribution of the mean will approach normality as sample size increases.

True

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

True

One implication of the central limit theorem is that a distribution of means will be less variable than a distribution of scores taken from the same population.

True

Standard error is the standard deviation of a distribution of means.

True

Standard error is the standard deviation of a distribution of means. Correct Answer

True

The distribution of means is less variable than the distribution of scores.

True

The standard deviation of a distribution of sample means is smaller than the standard deviation of the population when the sample size is 2.

True

The standard deviation of the z distribution is 1.0.

True

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

distribution of means

A z score is a measure of:

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

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

increases; decreases

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

increases; stays the same

A distribution of a small set of scores is _______ likely to be normally distributed than a distribution of a large set of scores.

less

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

means

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

normal

With large sample sizes, the shape of the distribution of the mean will be _______.

normal

As you increase the size of a sample, the distribution of the sample will approach the _______ as long as the underlying population is normally distributed.

normal curve

The distribution of scores in a a sample, drawn from a normal population, will approach normality as:

number of scores increases.

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

population standard deviation.

Two students recently took trigonometry 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 85 with a standard deviation of 5. The second student scored 65. Her class average was 50 with a standard deviation of 10. Which student did better?

second student because she performed better relative to her class

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

standard

When converting a z score into a raw score, we begin by multiplying the z score by the _______.

standard deviation

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

standard deviation units.

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

standard error

The z distribution is a normal distribution of _____ scores.

standardized

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

the central limit theorem

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

the central limit theorem; sample means

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

the mean of the distribution of raw scores.

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

the mean of the distribution of raw scores.

A normal distribution of standardized scores is the _______ distribution.

z

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

z

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

z = (M - µM)/ σM.

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

z score

The number of standard deviations a particular score is from the mean is the _______.

z score

Two scores that are based on two different scales can be directly compared once they are converted into _______.

z scores

A _______ is a z computed on a sample mean rather than a raw score.

z statistic

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

z statistic.

The symbol for the population mean is:

µ.

The symbol for the population standard deviation is:

σ.

The symbol for the standard error is:

σM.

On the first statistics exam, the class average was 72 with a standard deviation of 6. Reid scored 84. What is his z score?

2.0

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

16

A z score of -1.0 is equivalent to the _______ percentile.

16th

If a distribution of scores has a mean of 50 and a standard deviation of 10, then a score of 40 has a z score that is _____ standard deviation(s) _____ the mean.

1; below

Approximately 96 percent of scores fall within _______ standard deviation(s) of the mean.

2

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

X = z(σ) + µ.

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

always 0.

The primary assertion of the _______ is that a distribution of sample means approaches a normal curve as sample size increases.

central limit theorem

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

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