Deck 5: Describing Data With Z-Scores and the Normal Curve

Question 1

When two normal z-distributions are plotted on the same graph, what can we say about the relative frequency of each z-score?

A)It will always be the same.
B)It will always be different.
C)It depends on the raw score mean.
D)It depends on the raw score standard deviation.

Answer 1

A

Question 2

Which of the following statements accurately describes the sampling distribution of means?

A)The distribution of several sample means when an infinite number of samples of the same size N are selected from one raw score population.
B)The distribution of all possible sample means when a given finite number of samples of the same size N are selected from one raw score population.
C)The distribution of all possible sample means when an infinite number of samples of variously sized Ns are selected from several raw score populations.
D)The distribution of all possible sample means when an infinite number of samples of the same size N are selected from one raw score population.

Answer 2

D

Question 3

Given a normal distribution, as z­scores' absolute values increase, those z-scores and the raw scores that correspond to them occur

A)more frequently.
B)less frequently.
C)more frequently at first and then less frequently.
D)less frequently at first and then more frequently.

Answer 3

B

Question 4

For any approximately normal distribution, how can we find the relative frequency of the scores?

A)Convert the raw scores to z-scores and then use the standard normal curve.
B)Draw a graph of the raw scores and approximate the area under the curve.
C)Convert the raw scores to z-scores and then use the standard error of the mean.
D)Draw a graph of the raw scores and then use the standard error of the mean.

Question 5

Sally's z-score on a given measure is -2.5, where the population mean is 5 and the standard deviation is 1.5.What is Sally's raw score?

A)1.25
B)14
C)3.5
D)8.75

Question 6

In a z-distribution, the standard deviation will always be

A)greater than 1.
B)less than 1.
C)equal to 1.
D)equal to 0.

Question 7

A z-score of zero always means

A)the raw score does not exist.
B)the raw score exists, but is negligible.
C)the raw score almost never occurs.
D)the raw score is equal to the mean.

Question 8

We can use the standard normal curve as our model for

A)perfectly normal distributions only.
B)perfectly normal distributions only, when transformed to z-scores.
C)any approximately normal distribution, when transformed to z-scores.
D)any approximately normal distribution, when transformed to percentiles.

Question 9

Which of the following is not one of the things the relative frequency of z-scores allows us to calculate for corresponding raw scores?

A)Relative frequency
B)Percentile
C)Comparison against other variables
D)Values in terms of goodness or badness

Question 10

Your relative standing informs you

A)of how your scores compares with the sample or population from which it is derived.
B)of the significance of your score.
C)whether your score is from a sample or a population.
D)of surprisingly very little.

Question 11

The mean of the sampling distribution of means is always

A)greater than the population mean.
B)less than the population mean.
C)equal to the population mean.
D)the population mean divided by the square root of N.

Question 12

To evaluate a person for possible brain damage, a neuropsychologist gives the person a visual memory test and a reading test.To compare the person's performance across these two tests, what should the neuropsychologist do?

A)Graph the raw score distribution for each test on the same graph.
B)Calculate a z-score for each test.
C)Calculate z-scores for the sample means.
D)Find the simple frequency of the person's raw score for each test.

Question 13

A z­score communicates a raw score's

A)absolute magnitude.
B)distance from the mean in standard deviations.
C)direction from the standard deviation.
D)variability.

Question 14

Pat's last statistics test score was 72.If the instructor tells Pat the grade distribution was approximately normal, the class mean was 67, and the standard deviation was 3, which of the following is correct?

A)A score of 72 is never good.
B)Pat should be worried about this score, because many other students did better.
C)Pat should be fairly happy about this score, because many students did not do as well.
D)Pat should be ecstatic, because this is obviously one of the highest grades in the class.

Question 15

The distribution of z-scores is always

A)positively skewed.
B)negatively skewed.
C)the same shape as the distribution of raw scores.
D)more spread out than the distribution of raw scores.

Question 16

In sampling distributions, all the samples contain sets of raw scores

A)with the same variance.
B)from the same population.
C)with the same mean.
D)that are representative of the population mean.

Question 17

You should first transform X to z in all of the following cases except if you seek

A)X that marks a given relative frequency beyond X in tail.
B)percentile of an X above the mean.
C)percentile of an X below the mean.
D)relative frequency of scores beyond X in tail.

Question 18

z-scores can be calculated from

A)any data.
B)interval or ratio scores.
C)nominal or ordinal scores.
D)the range.

Question 19

Sampling distributions of means are always

A)approximately normally distributed.
B)positively skewed.
C)negatively skewed.
D)more variable than the population from which the samples were drawn.

Question 20

Chris wants to calculate a z­score for his own height.The average height in the class is 66 inches, and Chris's height is 62 inches.Chris calculated his z­score to be +1.5.What's wrong with his calculation?

A)The z-score is an inappropriate calculation here.
B)The z-score should be a higher number.
C)He didn't have the standard deviation.
D)The z-score should be a negative number.

Question 21

For the following set of scores, what is the z-score for a raw score of 23?

Question 22

For a z-score of 0.63, what is the area beyond the z-score in the tail?

Question 23

Jason's z-score for his time in the 10-K race was −3.If the raw score standard deviation was 5 and the mean running time for the competitors was 55 minutes, what was his raw score?

Question 24

The sample mean for a recent introductory psychology test was 78, and the sample variance was 9.If a student's z- score = -2.0, what was this student's raw test score?

Question 25

If raw scores ranging from 1 to 50 represented all the corresponding negative z-scores on the distribution, and raw scores ranging from 50 to 100 represented all the corresponding positive z-scores, what would be the total relative frequency of 50 to 100?

Question 26

For a distribution with = 50 and = 5, find the z-score for a raw score of 65.

Question 27

Suppose the population mean of some measure is 6 and the population standard deviation is 12.For a sample of 36, what is the standard error of the mean?

A)2
B)1
C)1/6
D)1/2

Question 28

For a distribution with = 50 and = 5, find the z-score for a raw score of 50.

Question 29

For a distribution with = 50 and = 5, find the raw score for z-score of +2.6.

Question 30

What raw score is at the 34th percentile 34.13 to be exact) when the mean of the distribution is 50 and the standard deviation is 4?

Question 31

For a z-score of 2.53, what is the area between the mean and the z-score?

Question 32

What is the area above a z­score of -0.48?

Question 33

The central limit theorem is particularly helpful in terms of understanding the basic nature of

A)normal distributions.
B)statistical significance.
C)measurement error.
D)statistical association.

Question 34

For a distribution with = 50 and = 5, find the raw score for z­score of -1.2.

Question 35

If there were 500 students in Jamal's class, approximately how many actual students scored higher than Jamal on
the quiz if Jamal had a z-score of −1?

Question 36

What is the area below a z-score of 1.40?

Question 37

For a z-score of 2.80, what is the area beyond the z-score in the tail?

Question 38

Another term for the standard deviation of the sampling distribution of means is known as

A)the standard error of the mean.
B)the central limit theorem.
C)relative frequency.
D)the sampling distribution of means.

Question 39

Using the appropriate values from the z-table, find the area for scores greater than z = +0.89.

Question 40

The sample mean for a recent introductory psychology test was 78, and the sample variance was 9.If a student
received a score of 82, what was this student's z-score?

Question 41

A sampling distribution of means for samples of students taking the SAT exam has a population mean of 500 and a standard error of 200.What proportion of sample means would fall between the population mean and a sample mean of 800?

Question 42

Suppose you know that a population standard deviation for a given measure is 18.For a sample of 169 subjects who have taken this measure, would would the standard error of the mean be?

Question 43

Briefly note the three basic procedures used to describe a sample mean from any underlying raw score population.

Question 44

Suppose you have a z-score value of 3.You also know the values of the mean of the sampling distribution and the standard error of the mean, both of which are 5.Would would be the sample mean?

Question 45

What is the area above a z-score of 1.96?

Question 46

If only the upper 30% of a normally distributed class passed a quiz for which the mean was 70 and the standard deviation was 10, what was the lowest score a student could have received and still have passed?

Question 47

Suppose a standardized test given to ninth-graders in Texas has a mean score of 125.Suppose at a given school in Texas, the ninth-graders have a mean score of 105.Why is this discrepancy present, and is it problematic?

Question 48

Barbara's z-score is -1.5.What does this score tell us relative to the mean of the population from which these scores originated?

Question 49

If your sense of direction, relative to a sample of college students, gave you a z-score of +1.5, what is your percentile?

Question 50

What is the standard deviation of any z-distribution?

Question 51

Consider the z-scores in parentheses) for the following individuals: Frank 0.5), Zoe -1.2), Jimmy 2.9), and Lilly - 3.3).Which of these individuals would have a) the lowest score, b) highest score, c) and most common score in the distribution?

Question 52

What percentage of scores in a normal distribution fall outside of the range of +3 SDs from the mean?

Question 53

For the following set of scores, what is the percentile for a score of 24?