SOC212 - Application Question #2
candi26oc
chapter_10_powerpoint.pptxWhen 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
<
