Mr. Weppler's Math Emporium (STAT 1253 Edition): Sampling Distributions, Central Limit Theorem and Confidence Intervals

Comic of the Day

Tip: The things themselves are all right, so who cares?

Announcements and Deadlines

Labs 6, 7, 8 and 10 due Thu Apr 16
Excel Final Exam on Thu Apr 16
Chapter 6-8 assignment (Moodle) due Thu Apr 23

Theory Exam (Chapter 6-8) is combined with Chapter 12 exam and will be on Thu Apr 23

This Week

1. Sampling Distributions and Central Limit Theorem

Central Limit Theorem Simulator

http://onlinestatbook.com/stat_sim/sampling_dist/

Set n=25 and run the simulator several hundred thousand times.

For any population distribution (normal, uniform, skewed, custom), the distribution of the sample mean, x̄, is normally distributed with the following properties:

the mean of the sample means approaches the population mean

the standard deviation of the sample means is less than the population standard deviation (it actually follows the formula below)

Lab 8 - Sampling Distributions
Lab 8 shows how a sample mean, x̄ (n=16 or 100) is usually close to a population mean, µ (N=10,000), and gets closer as n increases. You will use a VLOOKUP function to randomly sample from your payroll data.

3. Confidence Intervals

"A Mainstreet Technologies poll ... suggests Albertans are highly resistant to any tax hikes. Only 15 per cent of survey respondents say they’d favour increased taxes. Spending cuts are the preferred solution of 43 per cent."

"...automated phone survey of 3,184 Albertans."

"The Mainstreet Technologies survey is considered accurate within plus or minus 1.7 percentage points, 19 times out of 20."

http://calgaryherald.com/news/politics/alberta-sales-tax-the-most-detested-budget-solution-poll-says

Confidence Interval for Population Proportion, p

https://www.geogebra.org/m/kh7ndb2N

Confidence Interval for Population Mean, µ (σ known)

https://www.geogebra.org/m/NuypFzw9

Confidence Interval for Population Mean (σ unknown)

https://www.geogebra.org/m/HdXrD6Tw

For More Information

Sampling distribution
https://www.khanacademy.org/math/probability/statistics-inferential/sampling_distribution/v/sampling-distribution-of-the-sample-mean
https://www.khanacademy.org/math/probability/statistics-inferential/sampling_distribution/v/sampling-distribution-of-the-sample-mean-2
https://www.khanacademy.org/math/probability/statistics-inferential/sampling_distribution/v/standard-error-of-the-mean
https://www.khanacademy.org/math/probability/statistics-inferential/sampling_distribution/v/sampling-distribution-example-problem

Confidence Intervals (videos go beyond the content of this course)