OpenStax-CNX module: m47496 1

Confidence Intervals: Using

Spreadsheets to Explore and

Display Confidence Intervals*

Irene Mary Duranczyk

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 Spreadsheets and Excel to calculate and display Con�dence

Intervals.

1 Con�dence Intervals using Spreadsheets

In this section we will discuss techniques using spreadsheet for creating con�dence intervals for a one popu-lation mean, population standard deviation known; a one population mean, population standard deviationunknown: and for a population proportion,

1.1 Con�dence Intervals Formulas

You can set up a worksheet in Excel to compute the con�dence interval be using one of the following formulasin Excel or Google Spreadsheet

Function Excel Formula Google Spreadsheet formula

Con�dence interval for one popu-lation mean, population standarddeviation known.

=con�dence.norm(alpha, stan-dard deviation, number insample)

=con�dence(alpha, standard de-viation, number in sample)

Con�dence interval for one popu-lation mean, population standarddeviation unknown.

=con�dence.t(alpha, standarddeviation, number in sample)

No built in formula

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Con�dence interval for one popu-lation proportion.

There is no built in formula. .. we will calculate using modelbelow = p-hat±(critical value z-score*sqrt((p-hat*(1-p-hat)/n)

There is no built in formula. .. we will calculate using modelbelow = p-hat±(critical value z-score*sqrt((p-hat*(1-p-hat)/n)

Table 1

1.2 Displaying Con�dence Intervals:

To graph con�dence intervals the �Statistics Online Computational Resources (SOCR)� (just as in the previ-ous chapter) at http://socr.ucla.edu/htmls/SOCR_Distributions.html1 has in the dropdown menu for SOCRdistribution the normal distribution and for a Student's t-distribution. For a normal distribution, you willneed to have your mean and standard deviation and again your right and left cut o� values (which in thiscase will be your critical values). For a Student's t-distribution, you will need to have degrees of freedomand again your right and left cut o� values (which in this case will be your critical values). Below is a graphof the Student's t-distribution. We have used the example from 8.6 Two column Model step by step examplefor this demonstration. The degrees of freedom were 14 and a 95% con�dence interval. We used the t-tableto determine the left and right cut o� values. In this instance two tailed con�dence interval of 95% with 14degrees for freedom is minus and plus 2.145.

Figure 1

1http://socr.ucla.edu/htmls/SOCR_Distributions.html

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This next example is using the normal distribution for determining the con�dence interval for a populationproportion. The normal density curve here has the population proportion as the mean (p or p-hat) and thestandard deviation (the square root of (p(1-p)/n). We have demonstrated the example 8.8 to show youhow this looks in SOCR. For this problem the mean proportion was .842 and the critical z-value for a 95%con�dence interval was ± 0.032 or (0.81, 0.874).

Figure 2

1.3 Optional Classroom Exercise:

At your computer, try to use some of these tools to work out your homework problems or check homeworkthat you have completed to see if the results are the same or similar.

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