Answer:
A positive value of <em>z</em> indicates the sample mean is more than the population mean.
Step-by-step explanation:
The <em>z</em>-score or the standardized normal distribution score is defined as:
Here,
= sample mean
= population mean
= population standard deviation
<em>n</em> = sample size.
The value of population standard deviation is always positive since it is the square of the deviations of values from their mean.
Then if the value of <em>z</em> is positive or negative is determined by the value of and
.
- If <em>z</em> = positive, this implies that
That is the sample mean is greater than the population mean.
- If <em>z</em> = negative, this implies that
That is the sample mean is smaller than the population mean.
Thus, a positive value of z indicates the sample mean is more than the population mean.