Page 224 - Statistics for Dummies

208
Part IV: Guesstimating and Hypothesizing with Confidence
For example, you may want to compare the difference in average age of
Republicans versus Democrats, or the difference in average incomes of men
versus women. You estimate the difference between two population means,
, by taking a sample from each population (say, sample 1 and sample 2)
, plus or minus a
and using the difference of the two sample means
margin of error. The result is a confidence interval for the difference of two
. The formula for the CI is different depending on
population means,
certain conditions, as seen in the following sections; I call them Case 1 and
Case 2.
Case 1: Population standard
deviations are known
Case 1 assumes that both of the population standard deviations are known. The
formula for a CI for the difference between two population means (averages) is
, where and n are the mean and size of the first sample,
1
and the first population’s standard deviation, , is given (known); and n are
2
the mean and size of the second sample, and the second population’s standard
deviation, , is given (known). Here z* is the appropriate value from the stan-
dard normal distribution for your desired confidence level. (Refer to Table 13-1
for values of z* for certain confidence levels.)
To calculate a CI for the difference between two population means, do the
following:
1. Determine the confidence level and find the appropriate z*-value.

Refer to Table 13-1.
2. Identify , n , and ; find , n , and .
1 2
3. Find the difference, ( ), between the sample means.
4. Square and divide it by n ; square and divide it by n . Add the
1 2
results together and take the square root.
5. Multiply your answer from Step 4 by z*.
This answer is the margin of error.
6. Take x 1 x 2 plus or minus the margin of error to obtain the CI.
The lower end of the CI is minus the margin of error, whereas the
upper end of the CI is plus the margin of error.

3/25/11 8:14 PM
20_9780470911082-ch13.indd 208
20_9780470911082-ch13.indd 208 3/25/11 8:14 PM