Question

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 the z score be for a person whose self-esteem score was 101.6

Answer 1

The z-score for a person whose self-esteem score was 101.6 would be of -0.227.

Explanation:

Z-score:

In a set with mean
`\mu` and standard deviation
`\sigma`, the z-score of a measure X is given by:

`Z = (X - \mu)/(\sigma)`

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.

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.

This means that
`\mu = 108`

The standard deviation of self-esteem scores was 28.15

This means that
`\sigma = 28.15`

What would the z score be for a person whose self-esteem score was 101.6

This is Z when X = 101.6. So

`Z = (X - \mu)/(\sigma)`

`Z = (101.6 - 108)/(28.15)`

`Z = -0.227`

The z-score for a person whose self-esteem score was 101.6 would be of -0.227.