1. Click to edit Master title style Events Homework 1 Answer Keys are available (‘Homework’ link). More practice questions will be posted tonight (‘Homework’ link). THESE ARE OPTIONAL.

2. Click to edit Master title style Euro Cup 2015 FINAL Results.

3. Click to edit Master title style  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 Example

4. Click to edit Master title style Let’s try it…

5. Click to edit Master title style SDM Simulation Machine True μ: True σ: Sample Size (n): z cutoff - * = + * =  µ n z cutoff * + InOut X = Notice effect of n and σ on the size of the interval.

6. Click to edit Master title style 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,

7. Click to edit Master title style Let’s try it…

8. Click to edit Master title style Confidence Interval Simulation Machine True μ: True σ: Sample Size (n): z cutoff - * = + * =  X n z cutoff * + μ =μ =μ =μ = InOut Notice effect of n and σ on the size of the interval.

9. Click to edit Master title style Example Problem

10. Click to edit Master title style 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.

11. Click to edit Master title style Confidence Intervals (aka "margin of error") Suppose that your GPA sample mean is

12. Click to edit Master title style 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?

13. Click to edit Master title style Confidence Intervals (aka "margin of error") Lower Bound Upper 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?

14. Click to edit Master title style Confidence 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).

15. Click to edit Master title style Confidence 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.

16. Click to edit Master title style 95% Confidence Interval Example

17. Click to edit Master title style In-class Exercise Due 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.