SOC212 – Application Question #2

When to use a Z-test for one sample

How to compute the observed z value

Interpreting the z value and what it means

Statistics for People Who (Think They) Hate Statistics, Salkind, © 2012, Sage

What You Will Learn in Chapter 10

Examine differences between one sample and a population

Appropriate test statistic is a one-sample Z test

Statistics for People Who (Think They) Hate Statistics, Salkind, © 2012, Sage

One-Sample Z-Test

Determining Which Test to Use

Statistics for People Who (Think They) Hate Statistics, Salkind, © 2012, Sage

mean of the sample

population average

standard error of the mean

Statistics for People Who (Think They) Hate Statistics, Salkind, © 2012, Sage

Computing the Test Statistic

standard deviation for the population

size of the sample

Statistics for People Who (Think They) Hate Statistics, Salkind, © 2012, Sage

Computing the Standard Error of the Mean

Statistics for People Who (Think They) Hate Statistics, Salkind, © 2012, Sage

Example

 Size Mean Standard Deviation Sample 36 100 5 Population 1,000 99 2.5

Grades from a current earth science class compared to all earth science classes previously taught

A statement of null and research hypothesis

Null Hypothesis

Research Hypothesis

Set the level of risk (or level of significance or Type I error) associated with the null hypothesis

Select the appropriate test statistic

Statistics for People Who (Think They) Hate Statistics, Salkind, © 2012, Sage

One-Sample Z-Test: The Plan

Compute the test statistic value (called the obtained value)

Solve SEM first

Solve for z last

Determine the value needed for rejection of the null hypothesis using the appropriate table of critical values for the particular test (Table B.1)

Compare the obtained value and the critical value

Statistics for People Who (Think They) Hate Statistics, Salkind, © 2012, Sage

One-Sample Z-Test: The Plan

Decision Time!

If the obtained value is more extreme than the critical value, the null hypothesis CANNOT be accepted

Decision Time!

If the obtained value does not exceed the critical value, the null hypothesis IS the most attractive explanation

Statistics for People Who (Think They) Hate Statistics, Salkind, © 2012, Sage

One-Sample Z-Test: The Plan

represents the test statistics used

2.38 obtained value

indicates probability is less than 5%

Decision Time!

If the obtained value does not exceed the critical value, the null hypothesis is the most attractive explanation

Statistics for People Who (Think They) Hate Statistics, Salkind, © 2012, Sage

So How Do I Interpret…

Statistics for People Who (Think They) Hate Statistics, Salkind, © 2012, Sage

Excel’s Z.TEST Function

Statistics for People Who (Think They) Hate Statistics, Salkind, © 2012, Sage

Excel’s Z.TEST Function

Statistics for People Who (Think They) Hate Statistics, Salkind, © 2012, Sage

Excel’s Z.TEST Function

The one-sample Z-test is the most simple example of an inferential test

Understanding the one-sample Z-test provides a basis for more complex inferential tests

Statistics for People Who (Think They) Hate Statistics, Salkind, © 2012, Sage

Summary

X

Z

SEM

m

=

X

m

SEM

SEM

n

s

=

s

n

0

:

HX

m

=

1

:

HX

m

¹

2.38,.05

zp

=<

z

.05

p