 # 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. ### Essentials of Statistics for the B...

8th Edition
Frederick J Gravetter + 1 other
Publisher: Cengage Learning
ISBN: 9781133956570 ### Essentials of Statistics for the B...

8th Edition
Frederick J Gravetter + 1 other
Publisher: Cengage Learning
ISBN: 9781133956570

#### Solutions

Chapter
Section
Chapter 8, Problem 1P
Textbook Problem

## 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.

Expert Solution

a.

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

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

### Explanation of Solution

The z-score is,

z-value=MeandifferenceStandard error

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

Expert Solution

b.

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

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

### Explanation of Solution

Justification:

z-value=meandifferencestandard error×n

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

Expert Solution

c.

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

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.

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