1. STAT 1301 Calculating Chances Associated with the Sample Average Reading Handout 3

3. l STEP 1: Standard Units l STEP 1: Convert data value to Standard Units (z-score) - FORMULA - FORMULA for finding Standard Units: Value - AVG z = SD l STEP 2: l STEP 2: Look up z-scores in Normal Table Review: Using the Normal Table

4. “ DRAW PICTURE”

6. Facts About the Sampling Distribution of the Average l EV(X) = population AVG l SE(X) = (SD of Pop) / n l For n reasonably large, the distribution of X’s is approximately normal

7. Calculating chances for sample averages l Use the same 2-step procedure as before, but calculate z-scores using the formula value (of X) - EV(X) z = SE(X)

10. $485

11. Huge population, can’t get exact average Take SRS of 100 stations. Results of sample: AVG(sample) = $2.15 SD(sample) = $0.08 So, we estimate the average price for all stations in Texas to be about $2.15 How close is this likely to be to the true Texas average ? Example: Consumer reporter wants to know average price of unleaded gasoline in Texas on a certain day.

12. SE(X) measures this l What’s the problem here? –SE(X) depends on population SD –we don’t know population SD l How could you approximate the population SD? –use sample SD