Chapter 9 – Statistical Estimation Statistical estimation involves estimating a population parameter with a sample statistic. Two types of estimation: Point estimation Interval estimation

Point Estimation A single value is used as the estimate Example: Estimate the average weight of all turkeys (  ). Example: Estimate the average GPA of all CSULB students this semester (  ).

Errors of Estimation Sampling Errors Occur. This error is the difference between the value of the estimator and the value of the estimated parameter. Sampling Error = σ / √ n Increasing the n decreases the amount of error. Reasonable Bound on Error = 3 ( σ / √ n) Exercises from the book Example Problem 9-2, page 210 Example Problem 9-3, page 210 Problem 2, page 211 Problem 6, page 211 Problem 11, page 211

Interval Estimation Internal Estimate for a population parameter specifies a range of values. If we say that the true GPA of all CSULB students this semester is between 2.35 and 2.79, we are making interval estimation rather than a point estimation. Confidence level: a measure of confidence in estimation Depending on the level of confidence, the interval is known as 90% confidence interval or 95% confidence interval or 99% confidence interval where 90, 95, and 99% represent the confidence level.

What is confidence interval? If Alpha ( ά) is the probability that the estimate is in error, then (1- ά ) is the probability that the estimate is correct.

Interval Estimation on Population Mean Use the following formula: X + z ( σ / √ n ) ά / 2 X -- z ( σ / √ n ) ά / 2 Formula 9-1, page 213

Interval Estimation on Difference Between Two Population Means Interval estimation can be made on the difference between two population means. For example, the difference between the average height of all CSULB students and that of all CSUF students. Formula 9-5, page 214

More on intervals Interval Estimation about proportions Estimation can be made on population proportions. This can be done for one population proportion or for difference between two population proportions. Interval For One Population Proportion If one wants to estimate the true proportion of a population that meets a certain criterion, then formula 9-7, page 218 is used.

Interval for difference between two population proportions If you want to estimate true difference between two population proportion, use formula 9-10 (page 219).

Interval for difference…con’t Where p 1 = proportion of sample 1 p 2 = proportion of sample 2 n 1 = size of sample 1 n 2 = size of sample 2 z = as before ά/2 Example 9-7 (page )