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

Accepted Answer

To calculate the z-score, we use the formula:

z = (x - μ) / σ

where x is the individual's score, μ is the mean of the sample, and σ is the standard deviation of the sample.

Plugging in the values we have:

z = (104.28 - 135.2) / 28.15
z = -1.10

Therefore, the z-score for a person with a self-esteem score of 104.28 would be -1.10, which is option A.

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

Accepted Answer

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

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

Accepted Answer

D

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

Accepted Answer

Formula for calculating z-score is (x - μ) / σ
Here, Adam's score is 82 which is x.
Class average is 70 which is μ.
Standard deviation is 6 which is σ.

Putting the values in the formula we get,
z-score = (82 - 70) / 6 = 2.0

Therefore, the correct answer is D) 2.0

Question 5

The _____ curve forms a symmetrical and mathematically defined bell-shaped pattern.
A) asymmetric
B) unstandardized
C) normal
D) nonlinear

Accepted Answer

The question describes a normal curve, which is a specific type of symmetrical and mathematically defined bell-shaped pattern.

Question 6

The process of standardization involves the conversion of raw scores to _____ scores.
A) linear
B) standard
C) normal
D) nonlinear

Accepted Answer

Standard scores are created by converting raw scores into a standard form with a fixed mean and standard deviation. This allows for comparison among different sets of scores with different units and scales. Linear and nonlinear scores do not have fixed mean and standard deviation, while normal scores specifically refer to scores that are normally distributed.

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.

Accepted Answer

The mean of the distribution of z-scores is always 0, regardless of the mean and standard deviation of the original raw score distribution. This is because z-scores are calculated by subtracting the population mean from a raw score and then dividing by the population standard deviation, which centers the distribution around 0.

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

Accepted Answer

The z score of 1.6 represents a raw score that is farthest from the mean compared to the other given z scores. This is because a z score of 1.6 indicates that the raw score is 1.6 standard deviations above the mean, whereas the other z scores represent raw scores that are closer to the mean.

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.

Accepted Answer

To compare two scores measured on different scales, we need to transform them into a common scale. Z scores are the most common way to do this, as they transform raw scores into standard units of deviation away from the mean.

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

Accepted Answer

To calculate the z-score, we use the formula

z = (x - μ) / σ

where x is the individual score, μ is the mean, and σ is the standard deviation.

Plugging in the given values, we get

z = (40 - 50) / 10 = -1

Therefore, Jenna's z-score is -1.0. Option D is the correct answer.

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.

Accepted Answer

A z score represents the number of standard deviations a score is away from the mean. It is used to determine how unusual or typical a score is compared to the rest of the data set.

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.

Accepted Answer

A z-score of 0 represents the mean of the distribution of raw scores, so the person with a z-score of 0 would have a raw score equal to the mean.

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

Accepted Answer

To find the z-score, we use the formula z = (X - μ) / σ, where X is the score of interest, μ is the mean, and σ is the standard deviation. Plugging in the values, we get z = (50 - 60) / 10 = -1. This means the score of 50 is 1 standard deviation below the mean. Therefore, the correct choice is C.

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.

Accepted Answer

Without knowing the total number of questions on the test, or how the scores were standardized, it is impossible to compare the scores of the two students. Therefore, it is not possible to conclude that one student is smarter than the other or that they did equally well on the exam.

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.

Accepted Answer

According to the Central Limit Theorem, as the number of scores increases, the distribution of those scores will approach a normal distribution. This is because the mean and standard deviation of a large sample size will more accurately represent the population parameters, resulting in a bell-shaped curve.

Question 16

The z distribution _____ has a standard deviation of _____.
A) always; 0
B) sometimes; 0
C) always; 1
D) sometimes; 1

Accepted Answer

The z distribution always has a standard deviation of 1 because it is defined as the standard normal distribution with a mean of 0 and a standard deviation of 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

Accepted Answer

The z score formula requires the mean and standard deviation of the distribution to calculate a standardized score.

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

Accepted Answer

Adam's score is 10 points above the mean (60 - 50 = 10), and since the standard deviation is 10, his score is 1 standard deviation above the mean.

Question 19

The z distribution _____ has a mean of _____.
A) always; 0
B) sometimes; 0
C) always; 1
D) sometimes; 1

Accepted Answer

The z distribution always has a mean of 0, regardless of its standard deviation.

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

Accepted Answer

z score is calculated using the formula:
z = (x - μ) / σ

Where x is the raw score, μ is the mean and σ is the standard deviation.

In this question:
x = 45 (Adam's score)
μ = 50 (Class average)
σ = 10 (Standard deviation)

Plugging these values into the formula:
z = (45 - 50) / 10
z = -0.5

Therefore, Adam's z score is -0.5, which is closest to answer choice B (-0.5).

Quiz 6: The Normal Curve, Standardization and Z Scores

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

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.

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

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

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

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

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

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

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 z score is a measure of:

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

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.

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?

Distributions of scores approach the normal distribution as the:

The z distribution _ has a standard deviation of _.

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

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?

The z distribution _ has a mean of _.

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?