Chapter 15 and other topics

E-mail your edited chapter summary to jhl2881@students.kennesaw.edu as an attachment.

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Do not put your name on the document, but DO put your name in the email title.



SENIORS IN 1st and 2nd PERIODS: Go to Room 808 for class on Wednesday.

Pre-testing processing of the exam forms for AP testing (otherwise known as the Bubbling-in sessions) have started. Go to the theater at 7:30 in the AM or 3:30 in the PM to fill in your forms in anticipation of the big day.

Next test: Cumulative multiple choice test on Thursday, April 16.
Test after that: TUESDAY, April 21. (Unless you sign up for Monday afternoon free response testing.)



We plan to test on Chapter 15 on Tuesday, April 14. Until then we will be doing problems from old exams that relate to linear regression and inferences about the slope (the problems you Hawaii folks picked up on Tuesday!!!). We covered this stuff first semester when we did regression.

Our tentative plans for tests for the rest of the semester. . .

4/14 Chapter 15
4/15 Sophomore testing in the morning
4/16 Multiple choice test #1
4/21 Multiple choice test #2
4/23 Multiple choice test #3
week of April 20-24 Free response test after school 3:45 - 5:15 one day
May 5 the big one!
Sometime later Final exam

HW due Thursday
Write up the responses to the three free response questions discussed in class in your spiral notebooks.

Notes for the 2008 problem, part c: Follow their directions. Average the two proportions. For the standard deviation you will have to find the square root of the variance of the average. Yiles! Sounds difficult.

Variance of the average = 1/4 variance of x + 1/4 variance of y.

Chapter 14 Chi-square procedures

We have covered all the new material from this chapter. Your test will be on Tuesday, March 31.
HW for this weekend: AT LEAST three problems (not all odd) from the Chapter 14 chapter review. If you are struggling, do more problems. Bring all your CH 14 homework for credit on Tuesday.

Preview for after the test: We will be re-doing inference for regression (linear regression t-tests and confidence intervals) and power of the test.

Problems 11, 15, 16, and 24 are due Friday.

Problems 14.3, .4, .5, and .8 are due Wednesday.

HW due Tuesday: Using the data from your M&M bag, compare the sample distribution with the OLD theoretical distribution of BROWN 30%, RED 20%, YELLOW 20%, BLUE 10%, ORANGE 10%, and GREEN 10%. Perform a complete goodness of squares analysis of your data. If you misplaced your data, I guess you'll have to use a second bag of M&Ms. A complete analysis includes all the elements of SCAD.

Chapter 13 Two-sample tests

We're starting with tests of differences between two proportions. Usually our hypothesis is that there is no difference. Of course, we could look for a difference! Testing on Thursday, 3/19.

Bring all your HW from this chapter to the test on Thursday.

Problems 46 and 48 are due Wednesday.

Problems 13.41-44 are due Tuesday. Also, review your rules for variances. The variance of the difference of two means is equal to the sum of the variances of the two means. What is the variance of x-bar minus 3*y-bar if x and y are independent? Know your stuff.

Problems 15-18 should be done for Monday. Also, complete the hypothesis test from class:
Ho: mu E - mu N = 0 vs Ha: mu E -mu N < mu =" 7.26" dev =" 6.94" n =" 100" mu =" 9.55" dev =" 5.88" n =" 100" color="#ff0000">Your test on this chapter is on Thursday of next week.


HW due Thursday: Problems from the book 13.2, 3, 5, and 27, PLUS complete SCAD write-ups of the hypothesis test and confidence intervals for the differences in proportions from the census data linked below. We are looking for the difference between the % of adult Americans who have graduated from high school for women and for men.

Interesting 2-proportion statistic: http://www.census.gov/Press-Release/www/releases/archives/education/000818.html


People in the Lassiter area are happier than most: http://www.ajc.com/health/content/health/stories/2009/03/11/states_of_happiness_georgia.html?cxntlid=homepage_tab_newstab

HW due Wednesday: write up a complete (SCAD) response to the activity in class today. PLUS, read and create an outline for the second section of chapter 13.

Chapter 12 Tests about means and proportions

If you missed the test on Monday, please make it up Tuesday in room 214 at 7:20 AM. If you are involved in Model UN, please make it up in room 313 at 7:20 on Wednesday morning.

In this VERY SHORT chapter we practiced the methods that we use for simple tests in the real world.

Test is Monday!!! Please try out the online interactive software Crunch It that the publisher provides. Just search on Crunch It. It does a lot of the same things that Minitab does and in the same ways.

HW due Friday: Because the problems from last night were mostly odds, tonight's assignment involves evens. Do two even problems from the chapter review. Your test is Monday.


HW due Thursday: EITHER 12.9, 19, & 37 OR 12.3, 13, 23, 29, 31, & 34.
To get credit, all work must be shown. Copying out of the back of the book will not suffice.


HW due Wednesday: 12.15, .16, .18,. .24, & .26.
HW due Monday: Read through the first section, taking notes on the key differences between previous chapters and this one. Pay particular attention to the standard errors and the kind of test used as well as the changes to assumptions/conditions. Work problems 12.2, 12.4, 12.5, 12.6, and 12.12.

Chapter 11 Tests for significance

SIGN UP FOR AP EXAMS!

Check THIS website for an article about some of our superstars of statistics.


The applet on this webpage should be enlightening regarding Type I and Type II error. Scroll down the linked page a bunch until you find the yellow box entitled Statistical Errors Applet. Read the information in the little yellow box and click on the link where it says Applet 1. Statistical Errors near the little graph to display the applet. Move the box in the scroll bar at the top to change the value of alpha (the probability of a Type I error). In real life you can change this value, but pick your alpha before you collect your data! Otherwise, you might be accused of manipulating the data and giving statisticiansa bad name.
Now, move the middle of a NEW and IMPROVED distribution by sliding the box in the scroll bar at the bottom of the window. See what the yellow region looks like when you overlap the distributions. The yellow area represents the probability of a Type II error.
So, what effect does changing alpha have on the probabilty of a Type II error? When is beta maximized? When is it minimized?

TYPE I and TYPE II errors
PLEASE read the section in the book regarding these topics.

You will only be able to calculate a POWER or a BETA (the probability of a Type II error) when some NEW mean is introduced. The power of the test is the probability that the test will be able to distinguish between your original hypothesized mu and the newly proposed mu. The probability of an error is BETA.

To calculate BETA:
Find the boundaries of the FTR region for your original hypothesis. Find the probability that x-bar would fall between that lower bound and upper bound GIVEN the NEW mu and standard error of the mean. In calculator language [that you would NEVER write on a test] it would be normcdf(LB, UB, NEWmu, sigma of x-bar).


HW due Wednesday: 11.36-11.40. Your test is Thursday.


You should have worked problems 11.5, .6, .27, .28, .29, .30, .49, .50, & .51 by Tuesday. Your test is Thursday.

The excerpt in class today was from The Lady Tasting Tea by David Salsburg.

HW due Thursday: 11.3, 11.4, 11.6

Please note that (1) null hypotheses ALWAYS have an "equals" concept
(2) null and alternative hypotheses do NOT include statistics.

In inference testing, the results of our sample may make us reject the null hypothesis if they are so unlikely that they would be unbelievably unlikely due to randomness.

Please read through the top of page 693 AND register for the AP exam.

Chapter 10 Confidence Intervals

Your test on Chapter 10 will be Tuesday, February 17.
HW due Friday: Either problem 10.53 worked out in detail showing all work or problems 10.54 and 10.58 worked cout completely.
Have you hugged your study guide lately????
HW due Thursday: Problems 10.38 and .44. 1st and 2nd periods, please bring all HW from this week on Thursday.

Today we computed paired t confidence intervals for the difference in grip strength between right and left hands.

You can find the t* value for any number of df by using the calculator;
STAT TESTS T-INT Stats x-bar = 0, sx = sqrt df+1, n = df+1, conf level = whatever you need, like .95.

ALL students should have finished 10.28, 10.30, 10.31, and 10.31 PLUS the summary of the cautions. Have these with you on Wednesday.

HW for 1st and 2nd periods: Summarize the cautions of section 10.1 (pages 635-637) in your own words and work problems 10.28 and 10.30.
Periods 6 & 7: Work problems 10.7-10.10 PLUS summarize the cautions above.

The question was raised: Why do we use 2 sometimes and 1.96 other times for Z*? As you probably recall, approximately 95% of the data in a Normal distribution will fall within about 2 standard deviations of the mean, but that was just an estimate. The more precise number of standard deviations that form the 95% boundaries is 1.96. Use that whenever we are using Z procedures UNLESS we are just looking for a quick and dirty estimate. but NOT when we are constructing confidence intervals.

When do we use sx and when do we use sigmax? Sigma represents the population standard deviation, a number we rarely know. On the other hand, sx represents our sample standard deviation. When we do not know the population standard deviation we will use t procedures instead of z procedures.

And, of course, we divide by sqrt of n to convert these standard deviations into standard errors of x-bar.



Some web-based applets for Confidence Intervals: Rice Univ Freeman

HW due Friday--
1st and 2nd per: Problems 10.7-10.10 from the text. You should have already worked the problems from the REVIEW III on pages 610 and 611.
6th and 7th per: "Review III" questions following Chapter 9 on pages 610-611 in the text AND print one page from a confidence interval applet from the web and be able to explain it.

Key concepts from today: Approximately 95% of sample averages will fall within about 2 std dev/Sqrt(n) of the population mean. If we don't know what the population mean is, we might reason that our point estimate (x-bar) is a pretty good guess, and that 95% of the time, our sample averages will fall within 2 std dev/sqrt(n) of the true mean. Then the interval (x-bar minus 2*std dev/sqrt(n), x-bar plus 2*std dev/sqrt(n)) is our confidence interval or reasonable guess at the value of the population mean. About 95% of these intervals will capture the true mean. The distance from the mean to the upper bound (or event the lower bound) is the margin of error.

These are NOT true: 95% of the time this interval contains the mean. 95% of population means fall inside this interval. 95% of the time the mean falls between lower bound and upper bound. NONE of these are true, so DO NOT write these as interpretations of the confidence intervals.

Instead, we are 95% confident that the mean falls between the lower bound and the upper bound.

If you did not work problems from the review following Chapter 9, now is the time!!!!

Chapter 9 Sampling Distributions

If you missed the test on Tuesday, take it Tuesday PM at 3:30 in Mrs. Prestwood's classroom. HW for tonight: Do at least 5 of the 10 problems in REVIEW 3 which follows Chapter 9. Get ready for confidence intervals!!!!

http://www.stat.sc.edu/~west/javahtml/ConfidenceInterval.html


Prepare for the test by working problems from the text and by using a study guide (if you have one) to practice with multiple choice problems. You are welcome to come by in the morning to use a study guide in the classroom.

Your test on Chapter 9 is Tuesday, snow or no snow. Work lots of problems from the chapter. Be sure that you know how to check assumptions or conditions. Do you know when you are calculating probabilities for means and when you are calculating probabilities for proportions? You have to use the right conditions and formulas or you won't be answering the question.

Oh yeah, CiCi's Sunday. Super Bowl Sunday.

For Thursday, 1st and 2nd periods: Complete the questions from the AP exams that we looked at in class. The first one asked for (1) the probability that a measurement of a depth of 2 was negative when the error of the measurement was Normally distributed with mean 0 and std dev 1.5.
(2) What is the probability that at least one of three independent measurements from this distribution was negative?
(3) What is the probability that the average of three independent measurements from this distribution was negative?

Everybody needs to work problem 3 from the 2007 exam.


HW Problems 9.20, .21, 25., .26, &.29 due Wednesday.

HW Problems 9.19, 9.27, 9.30 due Tuesday.
Summary of the three sections of the chapter:
A sampling distribution is the distribution of the sample means of all possible samples of size n. As n (the sample size) increases, the variability of the sample means decreases.
When the underlying (original) distribution is Normally distributed, the sampling distribution for samples of any size n will be Normally distributed.
When the underlying (original) distribution is NOT Normally distributed, the sampling distribution for large sample sizes will be approximately Normally distributed. The closer the original distribution was to Normal, the smaller the sample size required to make the sampling distribution approximately Normally distributed.
These concepts can be applied easily to two cases: measures of x and sample proportions.
For measures of x: The mean of the sampling distribution of x bar is the mean of the underlying distribution of x. The standard deviation of the sampling distribution of x bar is the standard deviation of the underlying distribution /the square root of n.

For sample proportions: When np and nq are both > 10 and n is less than 1/10 of the population, the mean of the p hats is p and the standard deviation of the p hats is the square root of p*q/n AND the distribution of p hats is approximately normal.

< Link to a history of the penny.
Link to a more official history of the penny.

HW Problems 9.32 and 9.34.

I will NOT be available at Open House Thursday night. Please email me with any concerns or join us at CiCi's on Sunday.

HW due Friday, 1/23: 9.10, 9.12, 9.14. Students from per 1 and 2, email your averages to Mrs. L if you did not load them in class. Periods 6 and 7, look up the phrase "planned obsolescence."

This chapter requires you to recall some vocabulary from previous chapters.
HW due Thursday, 1/22: Problems 9.1, .7a-e, .9, .11, .13. You should read through the sections in order to understand the questions.
Also, periods 1 and 2, bring five results from mean(randBin(100,.5,100)).

Measures of central tendency
Median
Mean
Mode


Measures of dispersion (spread)
Range
Standard deviation
Variance
Interquartile range
Absolute deviation

Graphical displays
histogram
line graph
stem and leaf
box and whisker graph
probability density function
scatterplot
cumulative density function
dot plot
pie graph
bar graphs

Pictures speak louder than words

μ = population mean x bar = sample mean (unbiased estimator of mean)

If a sample is drawn at random from a population, the mean of the sample is an excellent estimator of the mean of the population.

σ = population standard deviation s = sample standard deviation

Recall that the calculation of s requires division by n-1 for some complicated reasons.

sx is the standard deviation of the distribution of x
is the standard deviation of the means of the samples of x

E[x] = E[ x bar]