Download Single Mean, Single Proportion Hypothesis Testing

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Single Mean, Single Proportion
Hypothesis Testing: Using
Spreadsheets for Calculations and
Display
∗
Irene Mary Duranczyk
Suzanne Loch
Janet Stottlemyer
This work is produced by OpenStax-CNX and licensed under the
†
Creative Commons Attribution License 3.0
Abstract
Basic directions on how to use Google Spreadsheet and Excel to calculate test results and display
density curves.
1 Hypothesis Testing: Single Mean, Single Proportion using Spreadsheets
In this section we will discuss techniques using spreadsheet for conducting an hypothesis test for one sample
mean, population standard deviation known; a one sample mean, population standard deviation unknown:
and for a one sample proportion,
1.1 Hypothesis Testing Formulas
You can set up a worksheet in Excel to compute the one sample tests by using one of the following formulas
in Excel or Google Spreadsheet
∗ Version
1.1: Aug 21, 2013 4:56 pm -0500
† http://creativecommons.org/licenses/by/3.0/
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Function
z-test:
for
population
one
Excel Formula
Google Spreadsheet formula
mean
=z.test(array,x,sigma) where ar-
=ztest(array,x,sigma) where ar-
deviation
ray is the sample data identify-
ray is the sample data identify-
ing the rst cell address and the
ing the rst cell address and the
last cell address in the data set,
last cell address in the data set,
x is the value you want to test,
x is the value you want to test,
and sigma is populations known
and sigma is populations known
standard deviation.
standard deviation.
sample
standard
known
t-test:
for a one sample mean
population
standard
deviation
=condence.t(alpha,
standard
No built in formula
deviation, number in sample)
unknown.
z-test: one sample proportion
There is no built in formula.
.
.
we will calculate using model
There is no built in formula.
.
.
we will calculate using model
below = p-hat±(critical value z-
below = p-hat±(critical value z-
score*sqrt((p-hat*(1-p-hat)/n)
score*sqrt((p-hat*(1-p-hat)/n)
Table 1
In an Excel or Google Spreadsheet you would arrange your data as demonstrated in the following columns.
The following is labeled as though it was an Excel or Google Spreadsheet.
Figure 1
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Quantitative Data in Column A
Figure 2
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Figure 3
1.2 Displaying Condence Intervals:
To graph T-test and Z-test use the Statistics Online Computational Resources (SOCR)(just as in the
previous chapter)at http://socr.ucla.edu/htmls/SOCR_Distributions.html
1
has in the dropdown menu for
SOCR distribution the normal distribution and for a Student's t-distribution.
For a normal distribution,
you will need to have your mean and standard deviation and again your right and left cut o values (which
in this case will be your critical values).
For a Student's t-distribution, you will need to have degrees of
freedom and again your right and left cut o values (which in this case will be your critical values). Below
is a graph of the Student's t-distribution. We have used the example from 8.6 Two column Model step by
step example for this demonstration. The degrees of freedom were 14 and a 95% condence interval. We
used the t-table to determine the left and right cut o values. In this instance two tailed condence interval
of 95% with 14 degrees for freedom is minus and plus 2.145.
1 http://socr.ucla.edu/htmls/SOCR_Distributions.html
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Figure 4
This next example is using the normal distribution for determining the condence interval for a population
proportion. The normal density curve here has the population proportion as the mean (p or p-hat) and the
standard deviation (the square root of (p(1-p)/n).
We have demonstrated the example 8.8 to show you
how this looks in SOCR. For this problem the mean proportion was .842 and the critical z-value for a 95%
condence interval was
±
0.032 or (0.81, 0.874).
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Figure 5
1.3 Optional Classroom Exercise:
At your computer, try to use some of these tools to work out your homework problems or check homework
that you have completed to see if the results are the same or similar.
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