1. Ex St 801 Statistical Methods Inference about a Single Population Mean (CI)

2. TYPES OF STATISTICAL INFERENCE ESTIMATION Answers the question What is the value of the population parameter? HYPOTHESIS TESTING Answers the question Is the parameter equal to a specific value?

3. PARAMETER ESTIMATION

4. TERMS AND DEFINITIONS An ESTIMATOR is a rule that tells us how to calculate the estimate based on sample information. A POINT ESTIMATOR of a parameter is a rule that estimates the parameter with a single value.

5. TERMS AND DEFINITIONS (contd.) An ESTIMATE is a number calculated using an estimator. An estimator is called UNBIASED if its average value is equal to the parameter being estimated. Otherwise, the estimator is called BIASED.

6. BIASED AND LARGE STANDARD ERROR

7. BIASED AND SMALL STANDARD ERROR

8. UNBIASED AND LARGE STANDARD ERROR

9. UNBIASED AND SMALL STANDARD ERROR

10. SOME EXAMPLES OF UNBIASED ESTIMATORS The SAMPLE MEAN is ALWAYS an unbiased estimator of the population mean. The SAMPLE MEDIAN is an unbiased estimator of the population mean if the distribution being sampled is symmetric about the population mean.

11. SOME EXAMPLES OF UNBIASED ESTIMATORS (contd.) The SAMPLE VARIANCE is ALWAYS an unbiased estimator of the population variance.

12. SOME EXAMPLES OF BIASED ESTIMATORS The SAMPLE MEDIAN is a biased estimator of the population mean if the distribution being sampled is not symmetric about the population mean. The SAMPLE VARIANCE is a biased estimator of the population variance if we use n in the denominator of the formula rather than n-1.

13. TERMS AND DEFINITIONS An INTERVAL ESTIMATOR of a parameter is a rule that provides two numbers that form an interval that is likely to contain the parameter. The interval is called a CONFIDENCE INTERVAL. (Smaller Value, Larger Value)

14. TERMS AND DEFINITIONS (contd.) The smaller value is called the LOWER CONFIDENCE LIMIT (LCL) and the larger value is called the UPPER CONFIDENCE LIMIT (UCL). The CONFIDENCE COEFFICIENT is the probability that a confidence interval will capture the parameter being estimated.

15. WHAT MIGHT BE EXPECTED TO HAPPEN IF 90% CONFIDENCE INTERVALS ARE CALCULATED FOR THE MEAN SAMPLE 10 SAMPLE 9 SAMPLE 8 SAMPLE 7 SAMPLE 6 SAMPLE 5 SAMPLE 4 SAMPLE 3 SAMPLE 2 SAMPLE 1 

16. CRITICAL VALUE Z   Z.025 = 1.96

17. LARGE SAMPLE CONFIDENCE INTERVAL FOR A SINGLE POPULATION MEAN

18. FACTORS AFFECTING THE “MARGIN OF ERROR” The value of the standard deviation (s). The value of the confidence coefficient (1-  ). The value of the sample size (n).

19. DETERMINING THE SAMPLE SIZE FOR A CONFIDENCE INTERVAL

20. NORMAL AND T-DISTRIBUTIONS NORMAL T-DISTRIBUTION

21. SMALL SAMPLE CONFIDENCE INTERVAL FOR A SINGLE POPULATION MEAN