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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.
Monday, February 23, 2009
Wednesday, February 04, 2009
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!!!!
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!!!!
Friday, January 30, 2009
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]
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]
Wednesday, January 14, 2009
Chapter 8 and the new semester
HW due Thursday: Problems 8.41, 8.43, and 8.44 from the text.
HW due Wednesday: Problems 8.45-8.50. Your test is Tuesday of next week--the day after the Dr. King holiday.
How are these questions similar? How are they different? What strategies would you use to answer each?
1. Of the 20 cell phones in a classroom, 30% do not accept text messaging. What is the probability that 3 out of a sample of 7 drawn from the 20 with replacement will not accept text messaging?
2. Of the 20 cell phones in a classroom, 30% do not accept text messaging. What is the probability that 3 out of a sample of 7 drawn from the 20 WITHOUT replacement will not accept text messaging?
3. Of the 200,000 cell phones in a metropolitan community, 30% do not accept text messaging. What is the probability that 3 out of a sample of 7 WITHOUT replacement will not accept text messaging?
HW due Tuesday, January 13: Probloems 8.19-8.24.
HW due Friday: 8.7, 8.10, 8.11, 8.13, & 8.16.
By Monday, make sure that all of the assigned homework has been done correctly and completely.
HW due Thursday: Problems 1-6 of Chapter 8. Each question requires that you explain how the 4 characteristics is satisfied. Also, define x in each setting. KEY: If your are not counting the number of successes (x) in n trials, it can't possibly be a binomial. If is IS, then check the rest of the conditions.
Yippee! We made to the home stretch.
We will begin Chapter 8 on Wednesday. Tuesday's HW is to complete as much of the crossword puzzle as possible. Some of the answers will become clearer as we progress through binomial and geometric distributions. The plan is to test on Chapter 8 next week and have a chapter test every 2-3 weeks thereafter. This way, we'll be able to dedicate the time after the break to review for the exam.
Let's see. Remove Mirage. Replace batteries. Ask parents to read and sign the syllabus. Bring paper, pencil, and calculator on Wednesday. Be safe.
Did I forget anything? :)
HW due Wednesday: Problems 8.45-8.50. Your test is Tuesday of next week--the day after the Dr. King holiday.
How are these questions similar? How are they different? What strategies would you use to answer each?
1. Of the 20 cell phones in a classroom, 30% do not accept text messaging. What is the probability that 3 out of a sample of 7 drawn from the 20 with replacement will not accept text messaging?
2. Of the 20 cell phones in a classroom, 30% do not accept text messaging. What is the probability that 3 out of a sample of 7 drawn from the 20 WITHOUT replacement will not accept text messaging?
3. Of the 200,000 cell phones in a metropolitan community, 30% do not accept text messaging. What is the probability that 3 out of a sample of 7 WITHOUT replacement will not accept text messaging?
HW due Tuesday, January 13: Probloems 8.19-8.24.
HW due Friday: 8.7, 8.10, 8.11, 8.13, & 8.16.
By Monday, make sure that all of the assigned homework has been done correctly and completely.
HW due Thursday: Problems 1-6 of Chapter 8. Each question requires that you explain how the 4 characteristics is satisfied. Also, define x in each setting. KEY: If your are not counting the number of successes (x) in n trials, it can't possibly be a binomial. If is IS, then check the rest of the conditions.
Yippee! We made to the home stretch.
We will begin Chapter 8 on Wednesday. Tuesday's HW is to complete as much of the crossword puzzle as possible. Some of the answers will become clearer as we progress through binomial and geometric distributions. The plan is to test on Chapter 8 next week and have a chapter test every 2-3 weeks thereafter. This way, we'll be able to dedicate the time after the break to review for the exam.
Let's see. Remove Mirage. Replace batteries. Ask parents to read and sign the syllabus. Bring paper, pencil, and calculator on Wednesday. Be safe.
Did I forget anything? :)
Tuesday, December 09, 2008
Chapters 6 and 7
Work at least 6 challenging, interesting problems from Chapter 6. If you don't choose challenging problems, then you're not going to be prepared for Thursday's test!
*** The Gator cheerleaders came out to practice with the band tonight and, when they were done, went into the gym and cheered for the freshman basketball team. Go Gators***
And they just mentioned both Venn diagrams and Simpson's Paradox on Numb3rs!
HW due Monday, December 8: Problems 7.55 and 7.58. The test will be on Thursday.
HW due Wednesday, December 3 - 7.32, .37, .38, and .39
HW for Monday- Problems 7.1-7.3 from the text CHAPTER SEVEN!
Please be safe. I will not be at CiCi's on Sunday, November 23. Also, please note that the email system is going to be down until we get back to school in December.
Have a happy Thanksgiving.
*** The Gator cheerleaders came out to practice with the band tonight and, when they were done, went into the gym and cheered for the freshman basketball team. Go Gators***
And they just mentioned both Venn diagrams and Simpson's Paradox on Numb3rs!
HW due Monday, December 8: Problems 7.55 and 7.58. The test will be on Thursday.
HW due Wednesday, December 3 - 7.32, .37, .38, and .39
HW for Monday- Problems 7.1-7.3 from the text CHAPTER SEVEN!
Please be safe. I will not be at CiCi's on Sunday, November 23. Also, please note that the email system is going to be down until we get back to school in December.
Have a happy Thanksgiving.
Monday, November 17, 2008
Chapter 5 - Generating and collecting data
Here's a website with some summary information about experimental design.
HW due Wednesday, 11/19/08: Problems 2006-5 and 2004-2 from the AP exams. Do the work on a separate piece of paper. No credit will be given for work done on the handout. If you missed class on Tuesday, swing by before school to get a copy or go to the AP website to retrieve a copy, but be prepared for class! Your test is on Thursday.
HW due Tuesday, 11/18/08: Problems 5.46-5.49. Your test on Chapter 5 is Thursday.
HW due Monday, 11/17/08: Problem 5, part c from the 2005 exam. The original question is found at www.collegeboard.com/apstudents.
A survey will be conducted to examine the educational level of adult heads of households in the United States. Each respondent in the survey will be placed into one of the following two categories:
(c) Since education is largely the responsibility of each state, the agency wants to be sure that estimates are available for each state as well as for the nation. Identify a sampling method that will achieve this additional goal and briefly describe a way to select the survey sample using this method.
Your answer must be written and complete and reflect your best reasoning.
Your test on this chapter is Thursday.
HW due Friday: 5.9, 5.10, 5.13, 5.14. Know how each of these types of bias occurs and what its implications are: response, non-response, voluntary response, wording, undercoverage. Also, how does convenience sampling lead to bias?
Know also how to conduct surveys using each of these methods:
Stratified random sample: Create layers of homogeneous groups and randomly sample from each.
Systematic random sample: Select every nth person for the survey.
Cluster sampling: Survey a smaller heterogeneous group that has characteristics similar to the entire population.
Simple random sampling of size n: (the ideal) use random methods that ensure that every person has the same likelihood of selection AND that every possible group of n people has the same likelihood of selection.
Your HW due Wednesday 11/12 is 5.1-5.5 (after reading the first four pages of the chapter).
Here are the questions that will be on the long form and the short form of the census in 2010. The actual date of the census will be April 1, 2010.
HW due Wednesday, 11/19/08: Problems 2006-5 and 2004-2 from the AP exams. Do the work on a separate piece of paper. No credit will be given for work done on the handout. If you missed class on Tuesday, swing by before school to get a copy or go to the AP website to retrieve a copy, but be prepared for class! Your test is on Thursday.
HW due Tuesday, 11/18/08: Problems 5.46-5.49. Your test on Chapter 5 is Thursday.
HW due Monday, 11/17/08: Problem 5, part c from the 2005 exam. The original question is found at www.collegeboard.com/apstudents.
A survey will be conducted to examine the educational level of adult heads of households in the United States. Each respondent in the survey will be placed into one of the following two categories:
- Does not have a high school diploma
- Has a high school diploma
(c) Since education is largely the responsibility of each state, the agency wants to be sure that estimates are available for each state as well as for the nation. Identify a sampling method that will achieve this additional goal and briefly describe a way to select the survey sample using this method.
Your answer must be written and complete and reflect your best reasoning.
Your test on this chapter is Thursday.
HW due Friday: 5.9, 5.10, 5.13, 5.14. Know how each of these types of bias occurs and what its implications are: response, non-response, voluntary response, wording, undercoverage. Also, how does convenience sampling lead to bias?
Know also how to conduct surveys using each of these methods:
Stratified random sample: Create layers of homogeneous groups and randomly sample from each.
Systematic random sample: Select every nth person for the survey.
Cluster sampling: Survey a smaller heterogeneous group that has characteristics similar to the entire population.
Simple random sampling of size n: (the ideal) use random methods that ensure that every person has the same likelihood of selection AND that every possible group of n people has the same likelihood of selection.
Your HW due Wednesday 11/12 is 5.1-5.5 (after reading the first four pages of the chapter).
Here are the questions that will be on the long form and the short form of the census in 2010. The actual date of the census will be April 1, 2010.
Thursday, November 06, 2008
Chapter 4 Examining Nonlinear Relationships
Due Friday 11/7/08: Problems 4.41-48 in the book. YOu'll need to read the section that precedes these questions. The test is on Monday. Don't wait until the last minute to work problems. [Check out the Barron's sudy guide, sections 4 and 5 for more problems.]
UPDATE: The Chapter 4 test has been postponed to Monday, November 10, but you still need to work problems!
HW due Wed 11/5/08: You should have worked at least 5 problems from the first section of the chapter plus problems 4.23 and 4.26. It would be helpful for you to work more problems, since your test is Thursday.
HW due Friday: Bongiorno! Problem 4.12, the pizza problem. Sorry for the delay. The CCSD filters wouldn't let me post from school. si I had to wait until I got home.
HW due Thursday: problem 4.5 plus at least one of 4.6, 4.8, and 4.10. Finish your worksheet from today.
HW due Wednesday: Write out comprehensive notes for Chapter 4.
The test will be the Thursday after the election day.
UPDATE: The Chapter 4 test has been postponed to Monday, November 10, but you still need to work problems!
HW due Wed 11/5/08: You should have worked at least 5 problems from the first section of the chapter plus problems 4.23 and 4.26. It would be helpful for you to work more problems, since your test is Thursday.
HW due Friday: Bongiorno! Problem 4.12, the pizza problem. Sorry for the delay. The CCSD filters wouldn't let me post from school. si I had to wait until I got home.
HW due Thursday: problem 4.5 plus at least one of 4.6, 4.8, and 4.10. Finish your worksheet from today.
HW due Wednesday: Write out comprehensive notes for Chapter 4.
The test will be the Thursday after the election day.
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