Question

determine whether the statement is true or false. if it is false, rewrite it as a true statement.

it is impossible to have a z-score of 0.

choose the correct answer below.

a. the statement is false. a z-score of 0 is a standardized value that is equal to the mean.
b. the statement is false. a z-score of 0 is a standardized value that is equal to the standard deviation.
c. the statement is true.
d. the statement is false. a z-score of 0 is a standardized value that occurs when the test statistic is 0.

Explanation:

Analyze the given statement

Using the Z-Score Interpretation knowledge point
The statement is: "It is impossible to have a z-score of 0."
A z-score measures the number of standard deviations a data value \(x\) is from the mean \(\mu\).

Apply the z-score formula

Using the Z-Score Calculation knowledge point

$$ z = \frac{x - \mu}{\sigma} $$

If the data value is equal to the mean (\(x = \mu\)), then:

$$ z = \frac{\mu - \mu}{\sigma} = 0 $$

Thus, a z-score of 0 is possible and occurs when the data value equals the mean. The statement is false.

Evaluate the multiple-choice options

Using the Z-Score Interpretation knowledge point

• Option A: Correctly identifies the statement as false and explains that a z-score of 0 is equal to the mean.
• Option B: Incorrectly states a z-score of 0 is equal to the standard deviation.
• Option C: Incorrectly states the statement is true.
• Option D: Incorrectly references a test statistic of 0.

Answer:

• A. The statement is false. A z-score of 0 is a standardized value that is equal to the mean. (Correct answer)
• B. The statement is false. A z-score of 0 is a standardized value that is equal to the standard deviation.
• C. The statement is true.
• D. The statement is false. A z-score of 0 is a standardized value that occurs when the test statistic is 0.