Z-Scores: A Comprehensive Guide for Psychology Students

Question 1

Which formula is used to calculate a Z-score?

Accepted Answer

Z = (X - μ) / σ

Answer

Z = (X - σ) / μ

Answer

Z = (μ - X) / σ

Answer

Z = (σ - X) / μ

Question 2

What does a negative Z-score indicate?

Accepted Answer

A score that is below the mean

Answer

A score that is above the mean

Answer

A score that is equal to the mean

Answer

A score that is not significant

Question 3

In a study of reaction times, the average was 500 milliseconds with a standard deviation of 100 milliseconds. If a participant had a reaction time of 650 milliseconds, what would their Z-score be?

Accepted Answer

2.5

Answer

1.5

Answer

3.5

Answer

4.5

Question 4

To calculate a Z-score, which formula should you use?

Accepted Answer

Z = (X - μ) / σ

Answer

Z = (X - μ) / μ

Answer

Z = (X + μ) / σ

Answer

Z = (X + σ) / μ

Question 5

What is the formula used to calculate a Z-score?

Accepted Answer

(X - μ) / σ

Answer

(X - μ) / σ^2

Answer

μ / (X - σ)

Answer

σ / (X - μ)

Question 6

What is the primary purpose of standardizing data using Z-scores?

Accepted Answer

To compare scores from different distributions

Answer

To increase the mean of the distribution

Answer

To decrease the variance of the distribution

Answer

To make the distribution normal

Question 7

A student scores a 75 on a test with a mean of 80 and a standard deviation of 5. What is the student's Z-score?

Accepted Answer

-1

Answer

0

Answer

1

Answer

2

Question 8

What is the fundamental difference between a raw score and a Z-score?

Accepted Answer

A raw score measures absolute performance, while a Z-score measures relative performance.

Answer

A Z-score represents absolute performance, while a raw score reflects relative performance.

Answer

Raw scores are primarily positive, unlike Z-scores, which can be negative.

Answer

Z-scores are exclusively positive, whereas raw scores can assume negative values.

Question 9

Which of the following formulas is utilized to calculate a Z-score?

Accepted Answer

(x - mean) / standard deviation

Answer

(x + mean) / standard deviation

Answer

(mean - x) / standard deviation

Answer

(standard deviation - x) / mean

Question 10

What does a Z-score of 0 represent?

Accepted Answer

The score is equivalent to the mean.

Answer

The score is less than the mean.

Answer

The score is greater than the mean.

Answer

The score is equivalent to the standard deviation.

Question 11

Which of the following is NOT a valid application of Z-scores?

Accepted Answer

Calculating the mean and standard deviation

Answer

Comparing scores from various distributions

Answer

Determining the likelihood of a score

Answer

Standardizing data

Question 12

Which formula is used to calculate a Z-score?

Accepted Answer

Z = (X - μ) / σ

Answer

Z = (X - μ) / s

Answer

Z = (X - s) / μ

Question 13

What is the formula for calculating a Z-score?

Accepted Answer

(X - μ) / σ

Answer

(μ - X) / σ

Answer

(σ - X) / μ

Answer

(μ - σ) / X

Question 14

What are the characteristics of a standard normal distribution?

Accepted Answer

Mean = 0, Standard Deviation (SD) = 1

Answer

Mean = 1, SD = 0

Answer

Mean = 1, SD = 1

Answer

Mean = 0, SD = 0

Question 15

Which Z-score represents a higher relative standing?

Accepted Answer

1.96

Answer

-2.33

Answer

0.56

Answer

-1.04

Question 16

What does a negative Z-score indicate? (Educational Level: Basic)

Accepted Answer

A score below the mean

Answer

A score above the mean

Answer

A score equal to the mean

Answer

A score within one standard deviation of the mean

Question 17

Which of the following is the formula for calculating a Z-score? (Educational Level: Basic)

Accepted Answer

(X - μ) / σ

Answer

(X + μ) / σ

Answer

σ / (X - μ)

Answer

(μ - X) / σ

Question 18

What does a Z-score represent? (Educational Level: Basic)

Accepted Answer

The number of standard deviations a score is above or below the mean

Answer

The standard deviation of a score

Answer

The probability of obtaining a given score

Answer

The difference between two scores

Question 19

What is the Z-score for a score that corresponds to the median of a distribution?

Accepted Answer

0

Answer

1

Answer

-1

Answer

2.5

Question 20

Which interpretation of a Z-score is most accurate?

Accepted Answer

It represents the distance from the mean in standard deviation units.

Answer

It indicates the probability of obtaining a particular score.

Answer

It reflects the difference between two scores.

Answer

It signifies the mean of a distribution.

Question 21

How can Z-scores be effectively used to identify outliers?

Accepted Answer

Identify scores that deviate from the mean by more than 2 standard deviations.

Answer

Identify scores that fall within 1 standard deviation of the mean.

Answer

Identify scores that significantly differ from others in the distribution.

Answer

Identify scores that are within the normal range.

Question 22

Which of the following best describes the purpose of a Z-score?

Accepted Answer

Converting raw scores into a standard scale for comparison

Answer

Predicting the probability of an event occurring

Answer

Determining the mean and standard deviation of a distribution

Question 23

The formula for calculating a Z-score is:

Accepted Answer

Z = (X - μ) / σ

Answer

Z = (X + μ) / σ

Answer

Z = (X - μ) / σ ** 2

Question 24

Which of the following is NOT a characteristic of a standard normal distribution?

Accepted Answer

Skewed shape

Answer

Mean = 0

Answer

Standard deviation = 1

Question 25

How do Z-scores standardize a data distribution?

Accepted Answer

Subtract the mean and divide by the standard deviation.

Answer

Add the mean and divide by the variance.

Answer

Multiply the mean and subtract the standard deviation.

Answer

Z-scores cannot standardize a data distribution.

Question 26

Which of the following is the formula for calculating a Z-score?

Accepted Answer

(X - μ) / σ

Answer

(X - σ) / μ

Answer

(μ - X) / σ

Answer

(σ - X) / μ

Question 27

What is the Z-score for a data point that is 2 standard deviations above the mean?

Accepted Answer

2

Answer

0

Answer

1

Answer

-2

Question 28

Which of the following Z-scores represents a data point that is at the mean?

Accepted Answer

0

Answer

-1

Answer

1

Answer

2

Question 29

What is the Z-score for a data point that is 1.5 standard deviations below the mean?

Accepted Answer

-1.5

Answer

-0.5

Answer

1.5

Answer

0

Question 30

Which of the following is a benefit of using Z-scores?

Accepted Answer

They allow for the comparison of data from different distributions.

Answer

They provide a perfect representation of the underlying distribution.

Answer

They eliminate the need for statistical inference.

Question 31

What is the formula for calculating a Z-score?

Accepted Answer

(X - μ) / σ

Answer

(μ + σ) / X

Answer

(X + μ) / σ

Answer

(σ - X) / μ

Question 32

Which of the following is the formula for calculating a Z-score?

Accepted Answer

(X - μ) / σ

Answer

σ / (X - μ)

Answer

(X - σ) / μ

Answer

μ / (X - σ)

Question 33

What is the purpose of a Z-score?

Accepted Answer

To express a raw score's distance from the mean in standard deviation units.

Answer

To determine the probability of an event occurring.

Answer

To calculate the mean of a dataset.

Question 34

A Z-score of +2.0 indicates that a raw score is:

Accepted Answer

Two standard deviations above the mean.

Answer

Twice the value of the mean.

Answer

Two standard deviations below the mean.

Answer

Two points above the mean.

Question 35

In a normal distribution, approximately what percentage of scores fall within one standard deviation of the mean (between Z = -1 and Z = +1)?

Accepted Answer

68%

Answer

95%

Answer

50%

Answer

99.7%

Question 36

A student scores 80 on an exam with a mean of 70 and a standard deviation of 5. What is their Z-score?

Accepted Answer

2.0

Answer

0.5

Answer

-2.0

Answer

1.0

Question 37

Two students take different versions of an exam. Student A scores 90 on an exam with a mean of 80 and a standard deviation of 10. Student B scores 85 on an exam with a mean of 75 and a standard deviation of 5. Which student performed better relative to their respective exam group?

Accepted Answer

Student B

Answer

Both students performed equally well.

Answer

Cannot be determined from the information given.

Answer

Student A

Question 38

A researcher wants to study the top 5% of performers on a cognitive task. What Z-score cutoff should they use to define this group, assuming a normal distribution of scores?

Accepted Answer

Approximately 1.645

Answer

1.0

Answer

0.5

Question 39

What is a potential limitation of using Z-scores?

Accepted Answer

They assume a normal distribution, which might not always be accurate.

Answer

They are difficult to calculate.

Answer

They are only useful for comparing scores within the same dataset.

Question 40

In psychological research, Z-scores are commonly used for:

Accepted Answer

Standardizing scores for comparison, identifying outliers, and determining the significance of findings.

Answer

Calculating the mean and standard deviation of a dataset.

Question 41

If a distribution has a mean of 50 and a standard deviation of 10, what raw score corresponds to a Z-score of -1.5?

Accepted Answer

35

Answer

65

Answer

60

Answer

40