AGENDA: GMLT #6 Tues, Mar 15 I’VE GOT TO GO. MY MOM ONLY USES MY FULL NAME WHEN I AM IN TROUBLE.

More Stat Humor for March 14th: Did you know that 3.14% of sailors are… PI-rates?

Advanced Placement Statistics Section 9.1: Sampling Distributions   EQ: How do we calculate the statistics for a sampling distribution?

DEADLINE TO REGISTER FOR AP STAT MOCK EXAM IS Friday, Mar 18

RECALL: Design --- planning how to obtain data Descriptive --- using numbers, tables, or graphs to organize and summarize data obtained. Inference --- make generalizations, decisions, and predictions based on data obtained.

Old Terms: Parameter --- fixed number, such as  or , which describe a population

NEW TERMS: Sampling Distributions – statistical values taken from all possible samples of the same size from the same population

Ex. You have three billiard balls, each with a number on it Ex. You have three billiard balls, each with a number on it. Two of the balls are selected randomly (with replacement) and the average of their numbers is computed. All possible outcomes are shown below in Table 1.

Frequencies of means for N = 2.

Describing Shapes of Distributions---SOCS Outliers – Center – Spread - symmetric and bell-shaped there appear to be no outliers an appropriate measure of center would be the mean, located at 2 an appropriate measure of spread would be standard deviation, which is 0.5774; the range is 2

statistical proportion to estimate Remember: You never really know parameters. You must use statistics to estimate them.

In Class p. 568 #1, #2: Use correct notation #1 b #2 a #2b

What does this notation mean? Ex. The height of young women varies approximately according to the N(64.5, 2.5). Recall: What does this notation mean? Normal Simulation Using your Graphing Calculator: Notation: randNorm (µ, σ, n) µ  population mean σ  population standard deviation n  sample size

2. [Set seed #9] Simulate the heights of 25 randomly selected women in this particular distribution. Store these values in L1. 64.5 2.5 25 Command: randNorm(_____,______,_____)L1 Plot a histogram of the 25 heights. Use the following dimensions for X and Y. Xmin =  - 4 Xmax =  + 4 XScl =  Ymin = -3 Ymax = 20

9. Create a modified box plot on top of your histogram.   10. Based on the appearance of the histogram and the box plot, would you say the distribution is symmetric? Our distribution is neither symmetric nor bell shaped. It appears to be left-skewed.

6. What do you think would happen to the shape of the distribution if we took samples of size n = 25 and found the mean of each sample? Our distribution of the sample means would show less variability and begin to approach the population parameter µ.

Conclusion about Sampling Distributions:

population > 10(sample) Variability --- describes spread of distribution population > 10(sample) Sample size gives better estimate of true parameter Sample sizes tend to have variability

Assignment p. 568 #1, 2 p. 577 #8, 9