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Chapter 11: Confidence Intervals – Large Samples
495
Table 11-2:
Summary information for
Example 11-11
Construct a 99% confidence interval for the difference between the
proportions for the remedial and nonremedial groups.
Solution:
Let
be the proportion of students who were successful from the
remediation group. Let
be the proportion of students who were successful
from the non-remediation group.
From the information given,
= 100,
= 40,
̂
= 0.70,
̂
= 0.40,
√
̂
̂
̂
̂
√
= 0.09,
= 0.01,
⁄
= 2.5758.
Thus, the 99% confidence interval estimate for the difference of the
proportions is (0.70 – 0.40)
2.5758
0.09 = 0.3
0.2318.
That is, we are 99% confident that the difference between the proportions for
the remedial and non-remedial groups will lie between 0.0682 and 0.5318.
Since both the lower limit and the upper limit for the interval are positive,
one may conclude that there is a “significant” difference between the
proportion for the remedial group and the proportion for the non-remedial
group. That is, for the statistics course, we can conclude that remediation did
seem to help the students do better than those students who did not obtain
remediation.
We can also use the
Large Sample Confidence Interval for the Difference
Between Two Population Proportions
workbook to help with the
computations.
Figure 11 – 16
shows the workbook output.