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StatisticsEssentials of Statistics for the Behavioral SciencesThe 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.BuyFind*arrow_forward*

8th Edition

Frederick J Gravetter + 1 other

Publisher: Cengage Learning

ISBN: 9781133956570

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.

The *z*-score is,

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

**Justification:**

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.

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

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