1. Confidence Interval Estimation for a Population Mean
Lecture 36
Section 10.4
Mon, Nov 5, 2007

2. (pt. est.)  (appropriate no. of st. devs.)
Confidence Intervals
To estimate , we will use confidence intervals, as we did when estimating p.
The basic form, as well as the theory, is the same as before:
(pt. est.)  (appropriate no. of st. devs.)

3. Confidence Intervals What is the point estimate for ?
What is the standard deviation for this estimator?
How do we determine the appropriate number of standard deviations?

4. Confidence Intervals
The confidence interval will be or

5. When to Use Z If Then use Z.
The population is normal (or nearly normal) and  is known, or
The population is not normal, but the sample size is at least 30,
Then use Z.

6. When to Use t If Then use t.
The population is normal (or nearly normal), and
 is not known,
Then use t.

7. Example
Example 10.4, p. 641.
Construct a 95% confidence interval for the true mean weight of such boxes.

8. Example Use Z. (Why?) n = 25. x = 9.82. Assume that  = 0.29. (Why?)
Level of confidence = 95%, so z = 1.96.

9. Example
The confidence interval is

10. TI-83 – Confidence Intervals
When the standard normal distribution applies, do the following.
Press STAT.
Select TESTS.
Select ZInterval.
A window appears requesting information.

11. TI-83 – Confidence Intervals
Select Data or Stats.
Assume we selected Stats.
Enter .
Enterx.
Enter n.
Enter the level of confidence.
Select Calculate and press ENTER.

12. TI-83 – Confidence Intervals
A window appears containing
The title “ZInterval”.
The confidence interval in interval notation.
The sample mean.
The sample size.

13. Example
Example 10.5, p. 643.
Construct a 99% confidence interval for the mean number of unoccupied seats.

14. Example Should we use Z or t? Why? n = 61. x = 12.6. s = 4.4.
Level of confidence = 99%. Find t.

15. Example
The confidence interval is

16. TI-83 – Confidence Intervals
To use t, do the following.
Press STAT.
Select TESTS.
Select TInterval.
A window appears requesting information.

17. TI-83 – Confidence Intervals
Select Data or Stats.
Assume we selected Stats.
Enterx.
Enter s.
Enter n.
Enter the level of confidence.
Select Calculate and press ENTER.

18. TI-83 – Confidence Intervals
A window appears containing
The title “TInterval”.
The confidence interval in interval notation.
The sample mean.
The sample standard deviation.
The sample size.