Events

• Homework 1 Answer Keys are available (‘Homework’ link).

• More practice questions will be posted tonight (‘Homework’ link). THESE ARE OPTIONAL.

Euro Cup 2015

• FINAL Results.

Suppose that the population mean is -2 and the population standard deviation is 8.

You run an experiment with 64 observations.

There is a 95% chance that your sample mean will be some value between

and

464

8222

n

064

8222

n

Example

Let’s try it…

SDM Simulation MachineSDM Simulation Machine

True True μμ::

True True σσ::

Sample Size (Sample Size (nn):):

zzcutoffcutoff

-- ** ==

++ ** ==

µ

nz cutoff **++

In Out

X =

Notice effect of n and σ on the size of the interval.

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This allows us to get a ‘margin for error’, or ‘confidence interval’ when we estimate the population mean from our sample mean.

Reversing the equations (doing some alegebra), there is a 95% chance that your population mean,

will be within two standard errors,

of your sample mean,

n

2

X

Let’s try it…

Confidence Interval Simulation MachineConfidence Interval Simulation Machine

True True μμ::

True True σσ::

Sample Size (Sample Size (nn):):

zzcutoffcutoff

-- ** ==

++ ** ==

X

nz cutoff **++

μμ = =

In Out

Notice effect of n and σ on the size of the interval.

Run 1 Expt

Refresh

Run 1000 Expts

Example Problem

Confidence Intervals(aka "margin of error")

The current mean GPA of college students nationwide is 2.65 and the standard deviation (σ) is 0.5.

What would be the mean GPA of (all) college students if universities were all free?

Study: Randomly sample 100 high school students, let them choose any university to attend for free. Calculate their mean GPA scores after 4 years.

Confidence Intervals(aka "margin of error")

Suppose that your GPA sample mean is

Confidence Intervals(aka "margin of error")

Suppose that your sample mean is

Confidence Intervals:

Find two values, one below your estimate of the population mean and the other above your estimate of the population value. What are the chances that the true population mean falls somewhere between these lower and upper bounds?

Confidence Intervals(aka "margin of error")

Lower BoundLower Bound Upper BoundUpper Bound

Suppose that your sample mean is

Confidence Intervals:

Find two values, one below your point estimate of the population mean and the other above your point estimate of the population value. What are the chances that the true population mean falls somewhere between these lower and upper bounds?

Confidence IntervalsConfidence Intervals

• How confident do you want to be that your interval "captures" the true value? (How much ‘risk’ are you willing to take in being wrong?)

• Let α ("alpha") be your acceptable uncertainty level (acceptable risk).

Confidence IntervalsConfidence Intervals

• Choose lower and upper bounds so that you have a 95% chance of "capturing" the true population mean.

• Remember: ‘cutoff’ z scores: 2 standard deviations to the left and right of the mean of a normal distribution captures 95% of the area under the curve.

95% Confidence Interval Example

100 5.0 9.2 nX

100

5.0*29.2 * 2

nX

0.31.09.2

100

5.0*29.2 * 2 -

nX

8.21.09.2

)0.3 , 8.2( :answer

In-class ExerciseDue by Thursday, 5pm.

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

• Click on “Download the Variables Trainer Program” link.

• Save the ‘zip’ file.

• Find it on your PC and click on it.

• EXTRACT THE FILES!!!!

• Click on “0 Click to Start Variables Trainer Program.exe”.

• Enter your PIN number in Questionnaire 2 on Polylearn.