Saturday, February 25, 2006
Chapter 10 test results
I will return tests to interested students at CiCi's on Sunday or in class on Monday. No, I do not pay students to attend CiCi's.
Sunday, February 05, 2006
SCAD for statistical inference problems
Georgia teens are probably familiar with SCAD-the Savannah College of Art and Design. Remembering this acronym can help you to include all of the parts of an inference problem (and maximize your points!!!!).
First you will address the SET-UP. This is where you write down all of the information that you pulled out of the question. You will define the hypotheses or the type of confidence interval, the statistics, and any parameters disclosed. You need to define your random variable. Keep in mind that mu and p do not vary; they are fixed. The values of x-bar or p-hat that you get from samples will vary. Therefore, you define your random variable x-bar or p-hat IN WORDS and symbols. Continue by identifying x-bar as the average value of ____________ from samples of size ______ or p-hat as the sample proportion of ___________________ with samples of size ______ (inserting the words you used when you defined your random variable and sample size). Define mu and p as the measures for the entire population. You can't use a symbol until you define it.
In hypothesis testing, be sure to use the values of mu or p in your hypotheses, not the statistics. For instance, if your were testing the proportion of students who lurk on the blog instead of writing to it when the experts think the proportion is 80%, but you think it is higher, your hypotheses are Ho: p = .8 and Ha: p > .8. Also, you only have an equals statement in the null hypothesis Ho.
The second portion of the complete answer is the ASSUMPTION or condition check. Yes, I know this is out of order, but at least you'll remember to do it! Most kids lose points by forgetting to do this or doing it poorly. The resource page of assumptions and tests in the appendix of the Barron's study guide provides a great summary of the conditions you need to check. Pay particular care to things like p or p-hat in the formulas. You have to use the right one to get satisfactory results. Don't just copy the items from the list and put check marks next to them. The readers know that you haven't actually done the check. Identify the reason why you did each test, like testing for 10n < population allows you to use simplified forms of the standard deviation. Know this. Write it down as your result after you plug in the values and test the conditions.
Of course the most satisfying part is the CALCULATION. Tell the reader what calculation you're doing, write out the formula, plug in the values, show how it is calculated, and write the numerical answer. Draw the picture. You can use your calculator to provide probabilities or z-values or t-values the same way you would use the standard normal or student's t distribution tables. Don't use them to magically provide the answer. You won't get any credit.
The final part is the DECISION. This would be the most important part to your employer. State your decision or explanation of the confidence interval in the terms of the problem, connnecting your numerical answers, the probabilities involved, and the actual words the author used. This is not time for fancy paraphrasing or concerns about plagiarism. The authors want an answer to their problem--not the answer to some related and colorfully-worded problem. Give them the facts, the probabilities, and a clear decision.
A local professor and excellent AP Statistics tutor, Michael Roty, once told me that his memory hook for answering statistics problems is "What did you do? Why did you do it? What does it mean?" I think that this summarizes the expectaions of the authors nicely. The SCAD structure should answer these questions.
First you will address the SET-UP. This is where you write down all of the information that you pulled out of the question. You will define the hypotheses or the type of confidence interval, the statistics, and any parameters disclosed. You need to define your random variable. Keep in mind that mu and p do not vary; they are fixed. The values of x-bar or p-hat that you get from samples will vary. Therefore, you define your random variable x-bar or p-hat IN WORDS and symbols. Continue by identifying x-bar as the average value of ____________ from samples of size ______ or p-hat as the sample proportion of ___________________ with samples of size ______ (inserting the words you used when you defined your random variable and sample size). Define mu and p as the measures for the entire population. You can't use a symbol until you define it.
In hypothesis testing, be sure to use the values of mu or p in your hypotheses, not the statistics. For instance, if your were testing the proportion of students who lurk on the blog instead of writing to it when the experts think the proportion is 80%, but you think it is higher, your hypotheses are Ho: p = .8 and Ha: p > .8. Also, you only have an equals statement in the null hypothesis Ho.
The second portion of the complete answer is the ASSUMPTION or condition check. Yes, I know this is out of order, but at least you'll remember to do it! Most kids lose points by forgetting to do this or doing it poorly. The resource page of assumptions and tests in the appendix of the Barron's study guide provides a great summary of the conditions you need to check. Pay particular care to things like p or p-hat in the formulas. You have to use the right one to get satisfactory results. Don't just copy the items from the list and put check marks next to them. The readers know that you haven't actually done the check. Identify the reason why you did each test, like testing for 10n < population allows you to use simplified forms of the standard deviation. Know this. Write it down as your result after you plug in the values and test the conditions.
Of course the most satisfying part is the CALCULATION. Tell the reader what calculation you're doing, write out the formula, plug in the values, show how it is calculated, and write the numerical answer. Draw the picture. You can use your calculator to provide probabilities or z-values or t-values the same way you would use the standard normal or student's t distribution tables. Don't use them to magically provide the answer. You won't get any credit.
The final part is the DECISION. This would be the most important part to your employer. State your decision or explanation of the confidence interval in the terms of the problem, connnecting your numerical answers, the probabilities involved, and the actual words the author used. This is not time for fancy paraphrasing or concerns about plagiarism. The authors want an answer to their problem--not the answer to some related and colorfully-worded problem. Give them the facts, the probabilities, and a clear decision.
A local professor and excellent AP Statistics tutor, Michael Roty, once told me that his memory hook for answering statistics problems is "What did you do? Why did you do it? What does it mean?" I think that this summarizes the expectaions of the authors nicely. The SCAD structure should answer these questions.
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