Chapter 8, Problem 1P

The value of the z-score in a hypothesis test is influenced by a variety of factors. Assuming that all other variables are held constant, explain how the value of z is influenced by each of the following:

a. An increase in the difference between the sample mean and the original population mean.

b. An increase in the population standard deviation.

c. An increase in the number of scores in the sample.

To determine

The effect of z-score on increase in difference between sample mean and original population mean.

Answer to Problem 1P

The z-score increases with the increase in difference between sample mean and original population mean.

Explanation of Solution

The z-score is,

$z\text{-value}=\frac{\text{Mean}\text{difference}}{\text{Standard error}}$

The z-score is directly proportional to the mean difference. So, increase in mean difference increases the z-value.

To determine

The effect on z-value of an increase in the population standard deviation

Answer to Problem 1P

The z-value decreases with an increase in the population standard deviation

Explanation of Solution

Justification:

$z\text{-value}=\frac{\text{mean}\text{difference}}{\text{standard error}}\times \sqrt{n}$

The z-value is inversely proportional to the standard deviation. So, increasing the standard deviation, then z-score decreases.

To determine

The effect on z-value of an increase in the number of scores in sample.

Answer to Problem 1P

The z-value decreases with an increase in the number of scores in sample.

Explanation of Solution

Increasing the number of z-scores in sample, decrease z.