Module 12: Confidence Intervals Part 2
In this module we'll pick up where we left off in Module 11.
This module is divided into 2 parts:
A.
Confidence intervals to estimate the population proportion.
B.
Confidence intervals to estimate the population variance.
Confidence intervals to estimate the population proportion are similar to the previous confidence intervals discussed in
Module 11. However, confidence intervals to estimate the population
variance
are significantly different and require the
use of the χ
2
(chi-square) distribution.

Module 12: Confidence Intervals Part 2
A.
Confidence intervals to estimate the population proportion
When constructing confidence to estimate the population proportion, we use the Z-Distribution used in in Module 11 to
estimate the population mean for large sample sizes.
This table, from slide 7 in Module 11, is applicable here.
As in Module, if you're constructing a confidence interval with a confidence level different from one of the examples in this
table, you will need to use Excel to determine the correct
factor using the method in the table above and discussed on
slide 6 in Module 11.
•
Confidence
α
α/2
Z
α/2
Z
α/2
0.99
0.01
0.005
Z
.005
2.5758
=NORMSINV(0.005)*-1
0.98
0.02
0.01
Z
.01
2.3263
=NORMSINV(0.01)*-1
0.96
0.04
0.02
Z
.02
2.0537
=NORMSINV(0.02)*-1
0.95
0.05
0.025
Z
.025
1.9600
=NORMSINV(0.025)*-1
0.90
0.10
0.05
Z
.05
1.6449
=NORMSINV(0.05)*-1
0.85
0.15
0.075
Z
.075
1.4395
=NORMSINV(0.075)*-1
0.80
0.20
0.10
Z
.10
1.2816
=NORMSINV(0.1)*-1

Module 12: Confidence Intervals Part 2
A.
Confidence intervals to estimate the population proportion
The formula for constructing confidence intervals to estimate the population proportion is as follows:
±
Where:
= the sample proportion.
If
is not given,
is calculated by
=
= 1 -
n = sample size (as always)
1= the Z-Factor as explained on the previous slide and in Module 11.
Confidence intervals to estimate the population proportion are very straightforward.
The only issue is whether the sample
proportion () is given or not, in which case
=
is the point estimate for the population proportion
is the confidence interval half width
•

Module 12: Confidence Intervals Part 2
A.
Confidence intervals to estimate the population proportion
Example 1
:
A study of 87 randomly selected companies with a telemarketing operation was completed. The study revealed
that 39% of those sampled had used telemarketing to assist them in order processing. Use this information to construct a 95%
confidence interval for the population proportion of telemarketing companies that use their telemarketing operation to assist
them in order processing.
[We know this is a proportion problem rather then a mean problem since it's asking you to construct a confidence interval
for the population proportion as opposed to constructing a confidence interval for the population mean as we did in Module
11. Always read the questions carefully so you don't get things confused]
From the text we know the following:
is given and
= .39; = .61 (1 - .39 = .61);
n = 87;
and that with a 95% level of
confidence, α/2 = .025.

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- Spring '14
- DebraACasto
- Normal Distribution, BURGER KING, α