The problem for Thursday's HW:
P-hat is 0.3, Ho: p = .25, Ha: p > .25
Your rival thinks that the sample indicates over 25% support for his program. He found 12/40 customers liked the idea. Write an email to the boss to enlighten him/her.
**********
The card problem:
Three cards are in a hat. One is white on both sides, one is red on both sides, and one has one white face and one red face. The cards are mixed and one is drawn from the hat and placed face down on the table without showing the underside. If the face up is red, what is the probability that the other face is also red?
Thursday, March 29, 2007
Monday, March 12, 2007
Chapter 12 Inference for proportions
Statistics in action. . .
Here's the basketball video.
http://viscog.beckman.uiuc.edu/grafs/demos/15.html
NCAA Brian's out in front with no way for anyone to catch up (I think). Pretty amazing. http://linnerstats.mayhem.sportsline.com/e
You'll need the password, which tells you who I think will win: gogators
Please try out this quiz and let me know how it works for you.
http://www.proprofs.com/quiz-school/quizview.php?id=567 :Basic stuff quiz
http://www.proprofs.com/quiz-school/quizview.php?id=585 :Which test do we do?
Cool sites for playing with proportions:
http://http://www.ltcconline.net/greenl/java/Statistics/HypTestProp/HypTestProp.htm
http://www.math.csusb.edu/faculty/stanton/m262/proportions/proportions.html
List of top engineering schools for recruiting as discussed in class (not in any particular order):
Cal Poly, Penn State, Penn, MIT, Florida A&M, Florida, RPI, Morgan State, Maryland, UCLA, Virginia, VA Tech, Iowa State, GA Tech, Howard, Colorado, Arizona, Cal – Berkley, North Carolina A&T, Puerto Rico, Michigan, Carnegie Mellon, Ohio State, Purdue, Illinois, Cornell, Texas, Texas A&M, Stanford, USC
This chapter is more of the same methods we saw in the last two chapters. You perform hypothesis tests and confidence intervals for proportions and for differences between proportions.
The tricky bits: (1) you have to keep track of which version of the proportion you will use for testing assumptions and for calculating standard deviations/std errors. Simply use the "best" information available. (2) Recognize when the inference is about proportions and when it is about measurements (chapter 11 methods). If you use X when you should have used p you let the reader know that you are confused.
When you have a 1 proportion hypothesis test, you have a hypothesized value for p that you use for both checking assumptions (conditions) and calculating the std dev.
When you are constructing a 1 proportion confidence interval, use the best info you have--the sample proportion. This is the lucky case where you just record the number of successes and the number of failures when you are checking the conditions. Because the estimator is used, we call the sqrt(p-hat(1- p-hat)/n) the standard error. Estimate------>>>>std error.
When you have a 2 proportion hypothesis test and you are testing to see if the two proportions are the same, well, doesn't that mean that the two proportions that you use in the std error calculation should be the same? In this case you generate a "pooled" estimator (Pooled sample proportion = sum of x / sum of n)to use for condition checking and for std error calculations. When checking conditions, use the pooled proportion * each value of n and (1 - the pooled proportion) * each value of n and make sure that each product is 5 or more.
On the other hand, when you are creating a 2 proportion confidence interval for the difference, you are not assuming that the proportions are the same, so the proportions must be checked separately and the formula for the std error resembles the formulas for two-sample conf interval std errors from Ch 11 a little bit. Checking conditions: for each sample check p-hat for that sample * sample size and (1-p-hat for that sample) * sample size.
Here's the basketball video.
http://viscog.beckman.uiuc.edu/grafs/demos/15.html
NCAA Brian's out in front with no way for anyone to catch up (I think). Pretty amazing. http://linnerstats.mayhem.sportsline.com/e
You'll need the password, which tells you who I think will win: gogators
Please try out this quiz and let me know how it works for you.
http://www.proprofs.com/quiz-school/quizview.php?id=567 :Basic stuff quiz
http://www.proprofs.com/quiz-school/quizview.php?id=585 :Which test do we do?
Cool sites for playing with proportions:
http://http://www.ltcconline.net/greenl/java/Statistics/HypTestProp/HypTestProp.htm
http://www.math.csusb.edu/faculty/stanton/m262/proportions/proportions.html
List of top engineering schools for recruiting as discussed in class (not in any particular order):
Cal Poly, Penn State, Penn, MIT, Florida A&M, Florida, RPI, Morgan State, Maryland, UCLA, Virginia, VA Tech, Iowa State, GA Tech, Howard, Colorado, Arizona, Cal – Berkley, North Carolina A&T, Puerto Rico, Michigan, Carnegie Mellon, Ohio State, Purdue, Illinois, Cornell, Texas, Texas A&M, Stanford, USC
This chapter is more of the same methods we saw in the last two chapters. You perform hypothesis tests and confidence intervals for proportions and for differences between proportions.
The tricky bits: (1) you have to keep track of which version of the proportion you will use for testing assumptions and for calculating standard deviations/std errors. Simply use the "best" information available. (2) Recognize when the inference is about proportions and when it is about measurements (chapter 11 methods). If you use X when you should have used p you let the reader know that you are confused.
When you have a 1 proportion hypothesis test, you have a hypothesized value for p that you use for both checking assumptions (conditions) and calculating the std dev.
When you are constructing a 1 proportion confidence interval, use the best info you have--the sample proportion. This is the lucky case where you just record the number of successes and the number of failures when you are checking the conditions. Because the estimator is used, we call the sqrt(p-hat(1- p-hat)/n) the standard error. Estimate------>>>>std error.
When you have a 2 proportion hypothesis test and you are testing to see if the two proportions are the same, well, doesn't that mean that the two proportions that you use in the std error calculation should be the same? In this case you generate a "pooled" estimator (Pooled sample proportion = sum of x / sum of n)to use for condition checking and for std error calculations. When checking conditions, use the pooled proportion * each value of n and (1 - the pooled proportion) * each value of n and make sure that each product is 5 or more.
On the other hand, when you are creating a 2 proportion confidence interval for the difference, you are not assuming that the proportions are the same, so the proportions must be checked separately and the formula for the std error resembles the formulas for two-sample conf interval std errors from Ch 11 a little bit. Checking conditions: for each sample check p-hat for that sample * sample size and (1-p-hat for that sample) * sample size.
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