# Chapter6-IntroductiontoInference - CHAPTER 6 WELCOME TO...

• Notes
• 48

This preview shows page 1 - 10 out of 48 pages.

CHAPTER 6 – WELCOME TO INFERENTIAL STATISTICS STAT 200
Outline Estimation Point Estimation Confidence Intervals Hypothesis Testing The Z-test Types of Error P-value 2 STAT 200 - Introduction to Statistics
In Reality… STAT 200 - Introduction to Statistics 3 In the last chapter we explored the sampling distribution of of the sample proportion and sample mean. Essential to calculating the probability of these sample values was the knowledge of the true proportion or mean. In reality, in most situations we don’t know the population mean or proportion.
Estimation STAT 200 - Introduction to Statistics 4 If we don’t know the population parameters, we’ll want to get information on what their values may be. The sample values contain information about the unknown parameters. The act of using samples to get an educated guess value for the unknown parameter is called Estimation.
More Estimation STAT 200 - Introduction to Statistics 5 Estimator:The formula used to obtain the “guess” for the value of the parameter. An estimator is a random value. Thus we can characterize its behavior with a sampling distribution? Estimate:A realization of the estimator. It is an actual guess at the value of the parameter. An estimate is a fixed value. An estimate by itself is called a point estimate The sample mean and sample proportion are both estimators.
Duck Billed Platypuses STAT 200 - Introduction to Statistics 6 A scientist is trying to find out the average poison charge in duck-billed platypuses. These funny mammals have two spikes near their hind legs. From 10 sampled platypuses he finds that the sample average is 3.7 ml per platypus. (3.0+4.1+1.9+3.8+4.2+4.5+3.9+4.4+3.7+3.5)/10
A Desirable Quality of Estimators STAT 200 - Introduction to Statistics 7 Definition:An estimatoris called unbiasedif its expected value is equal to the population parameter it is estimating. From the estimators we have seen, the following are unbiased estimators for , 2and p respectively, ˆp=Xn
The Standard Error STAT 200 - Introduction to Statistics 8 Reporting an estimate by itself may not be informative enough. We reported a sample mean of 3.7 ml for the platypus example, but this does not indicate how precise the estimate is. How surprised would we be to find out the true mean was 0.1 ml away from the estimate? 1 ml? 5 ml? Definition:The standard error of an estimator is its estimated standard deviation.
Types of Estimation STAT 200 - Introduction to Statistics 9 We estimate the ‘true’ mean (µ) using the sample mean ( ), but we understand that there is sampling variabilityassociated with our point estimate. A confidence interval provides a range of possible values for the parameter of interest. The interval uses both the point estimate and its standard error.
• • • 