1. Independent Samples: Confidence Intervals
Lecture 40
Sections 11.4 – 11.5
Wed, Apr 11, 2007

2. Confidence Intervals
Confidence intervals for 1 – 2 use the same theory.
The point estimate isx1 –x2.
The standard deviation ofx1 –x2 is
or approximately

3. Confidence Intervals The confidence interval is or
( known, large samples)
( unknown, large samples)
( unknown, normal pops.,
any size samples)

4. Confidence Intervals The choice depends on Whether  is known.
Whether the populations are normal.
Whether the sample sizes are large.

5. Example
Find a 95% confidence interval for 1 – 2 in Example 11.4, p. 699.
x1 –x2 = 3.2.
sp =
Use t =
The confidence interval is
3.2  (2.101)(2.259) = 3.2  4.75.

6. The TI-83 and Means of Independent Samples
To find a confidence interval for the difference between means on the TI-83,
Press STAT > TESTS.
Choose either 2-SampZInt or 2-SampTInt.
Choose Data or Stats.
Provide the information that is called for.
2-SampTTest will ask whether to use a pooled estimate of . Answer “yes.”

7. Confidence Intervals for p1^ – p2^
The formula for a confidence interval for p1^ – p2^ is
Caution: Note that we do not use the pooled estimate for p^. because we are not assuming that p1 = p2.

8. TI-83 – Confidence Intervals for p1^ – p2^
Press STAT > TESTS > 2-PropZInt…
Enter
x1, n1
x2, n2
The confidence level.
Select Calculate and press ENTER.

9. TI-83 – Confidence Intervals for p1^ – p2^
In the window the following appear.
The title.
The confidence interval.
p1^.
p2^.
n1.
n2.

10. Example
Find a 95% confidence interval using the data in the gender-gap example.