1. Confidence Interval of the Mean – Population St. Dev Unknown
T Interval

2. Objective
Construct a confidence interval with a population standard deviation NOT known and Find Sample Size.

3. Can Estimate Population Parameters from Sample Statistics
Relevance
Can Estimate Population Parameters from Sample Statistics

4. T Distributions……
Many times the population standard deviation is NOT known and the sample size is LESS THAN 30. Then, you must use a t-distribution.

5. Characteristics of t……
t distributions have the same characteristics as z’s except that they are based on degrees of freedom.

6. Degrees of Freedom
Values that are free to vary after a sample statistic has been computed.
df = n - 1
Example:
The mean of 5 #’s is 10 –- 4 of the 5 #’s are free to vary BUT the 5th number must be a specific value in order to get a sum of 50. df = 5-1=4

7. Confidence Interval for a T-Distribution (Still Means!)
Now the z is a t and now the sigma is an s

8. Practice….. Find for a 95% confidence level when n=22. df = n – 1
in calc:
invT(.025,21)
Read

9. You Try Find for a 99% confidence and a sample size of 14. df = n – 1
-in calculator:
invT(.005, 13).

10. Example……
Ten randomly selected cars were stopped and tread depth of the right front tire was measured. The mean was 0.32 inches and the st. deviation was Find the 95% confidence interval.

11. Substitute Values:

12. You Try
In a random sample of 10 adults from the U.S., the mean waste generated per person per day was 4.3 pounds and the st. deviation was 1.2 pounds. Find the 90% confidence interval.

13. Answer……

14. Example……
The pulse rates for 13 adult women were: 83,58,70,56,76,64,80,76,70,97, 68,78,108
Find the 90% CI.

15. Answer……
Put #’s in L1
Press Stat, Calc, One-Var Stats L1

16. You Try…… The SAT scores for 12 high school students are:
1424, 1223, 987, 692, 947, 723, 837, 721, 747, 540, 623, 1445
Construct the 99% confidence interval for the population mean.

17. Answer……

18. Extra Example…… The GPA for 15 students are listed below:
2.3, 3.3, 2.6, 1.8, 0.2, 3.1, 4.0,
0.7, 2.3, 2.0, 3.1, 1.4, 1.3, 1.6,
1.6
Construct a 90% confidence interval.

19. Answer……