Question

z Scores If your score on your next statistics test is converted to a z score, which of these z scores would you prefer: -2.00, -1.00, 0, 1.00, 2.00? Why?

Short answer

A z-score equal to 2.00 will be preferred because it is a positive value, which depicts that the test score attained is 2 standard deviations greater than the mean score.

Step-by-step solution

Given information

Four z-scores corresponding to the test score obtained in a statistics test are given as -2.00, -1.00, 0, 1.00, and 2.00.

Z-score

Az-score gives an overall idea of how many standard deviations a given observation is above or below the mean value.

In the case of a sample, a z-score is obtained as:

$z=\frac{x-\overline{x}}{s}$

Here,

x is any data value.

$\overline{x}$ is the sample mean.

s is the sample standard deviation.

Apositive z-score indicates that the value is above the mean, and anegative value indicates that the data value is below the mean.

Determine the preferred z-score

Here, a higher positive z-score implies that the test score obtained is significantly above the mean test score.

Since2.00 is the highest positive value among all the four values, a z-score of 2.00 is preferred over the others.