Homework 1 due today by 5pm…

Your First Hypothesis Test:Is the Coin Biased towards

HEADS?

• Go to stat217.com, ‘stats link’ page.

• Find: Coin Flipping Hypothesis Test

• Read the instructions then Click the Link.

Inferential Statistics: Step OneInferential Statistics: Step One

If you were to run your experiment over and over again, how much variability would there be in the sample means that you get?

How surprised should I be about How surprised should I be about my data if my Research my data if my Research Hypothesis is FALSE?Hypothesis is FALSE?

Demo Program 5

• Go to stat217.com, ‘stats link’ page.

• Click on “Download Demo Program 5”.

• Save the ‘zip’ file.

• Find it on your PC and click on it.

• EXTRACT THE FILES!!!!

• Click on “0 Click to Start Living the Lecture Part 5.exe”.

• Try the program. Do you understand the difference between the population mean or standard deviation and mean or standard deviation of the sampling distribution of the mean? What is the effect of changing the sample size of the experiment on these values?

The Sampling Distribution of the Mean

• If you run your experiment over and over again, the mean of the sample means will be equal to the population mean.

The Mean of the Sampling Distribution of the Mean

XX

The Standard Deviation of the Sampling Distribution of the Mean

• If you run your experiment over and over again, the standard deviation of the sample means will be equal to the standard deviation of the population divided by the square root of the sample size.

The Standard Error of the Mean

(The standard deviation of the sampling distribution of the mean)

nX

Instructor’s Note: Many problems will require you to compute (or think of) this new standard deviation. MANY students forget to divide by the square root of n.

The Sampling Distribution of the Mean

• If you run your experiment over and over again, the distribution of the sample means will (probably) be a bell-shaped curve (the Normal Distribution).

Inferential Statistics: Next StepInferential Statistics: Next Step

The Normal Distribution

• Describes a Population

• Is unimodal, symmetric

• Is “Bell-shaped”

• Has TWO parameters:

, (remember this!)

Normal distributions are lumps of clay (of same quantity).

tall and skinny

short and fat

Other Important Facts:

1. They never actually touch the X-axis --so every score is possible, from .to

Normal distributions are lumps of clay (of same size).

tall and skinny

short and fat

Other Important Facts:

2. The total area underneath them is always 1.

Very Important Fact About Normal Distributions

The area under the curve between the mean and any other point (left or right) depends only on the number of standard deviations between these two points.

Very Important Fact About Normal Distributions

The number of standard deviations between the mean and any other possible score (any ‘raw’ score) is the “z score” for this other (raw) score.

Web Exercise Sample Statistics are estimates of

Population Statistics.

• Complete at least 3 problems to get credit for the exercise.

• Save money to compete for your country (and win “special” prizes…).

• Log in as a Guest to practice if you like….