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Chapter 11: Confidence Intervals – Large Samples
Example 11-16:
A researcher wishes to study the difference between the
average score on a standardized test for students who major in marketing and
art. The standard deviation for the scores is 5 for both groups of students.
How large a sample (equal in this case) must the researcher use if she wishes
to be 99 percent certain of knowing the difference of the average of the
scores for the two populations to be within
3 points.
Solution:
We are given
= 0.01 and
E
= 3,
1
=
2
= 5. Since
= 0.01,
then z
/2
= 2.575829. Thus,
n
= (2.575829/3)
2
(5
2
+ 5
2
) = 36.86053
37.
That is, the researcher should sample at least 37 students from each group.
Note:
The formulas for non-equal sample sizes are much more complex
when considering confidence intervals (inferences) for the differences of
parameters.
We can use
the Large Sample Confidence Interval for the Difference
between Two Population Means
to solve for the sample size. The output is
shown in
Figure 11-23
.