Topics on the AP Stat 1st Semester Final Exam
Types of graphs, their advantages and disadvantages, their interpretations
Measures of center and spread, their calculation, their different meanings, and their uses
Measures of position, converting back and forth among different measures (i.e. percentile, observed value, and z-value)
Probabilities associated with continuous random variables (area under the curve, normalcdf, empirical rule, Chebyshev’s theorem)
Probabilities associated with discrete random variables, multiplication property, addition property, independence, conditional probabilities
Special discrete random variables—binomial and geometric distributions
Relationships in two variables – linear regression, residuals, interpreting regression output, correlation coefficient, coefficient of determination
Means and standard deviations of combinations and transformations of random variables
Design of surveys, types of bias, types of sampling
Design of experiments, methods of randomizing, methods of control, matched pairs design, blocking, causation
Vocabulary: for instance, outliers, clusters, gaps, population, sample, variance, influential observations
Answer the following two questions on two separate sheets of paper. Your response to question one will be graded as a small test grade. Your response to question two will be the free response part (take-home portion) of your final exam. Your answers may be hand-written or typed, but must be legible and complete. Computed numbers that are unsupported by their calculations will be given no credit. You may NOT work together on this assignment.
Question One: Using an example from the second half of your selected book (Bringing Down the House, Freakonomics, etc.), explain a specific connection to one of the topics in the list of exam topics above. You may get creative with your product for this question. It may be in the form of a Powerpoint, a 9”x12” poster, or other appropriate written or mixed media form. Interpretive dance is not appropriate.
Question Two: Answer the problem handed out in class on a separate sheet of paper. You must work alone on this problem.
Monday, December 13, 2010
Monday, December 06, 2010
Distributions of Random Variables
11/19/2010
We're combining parts of chapters 6-8 to build on students' prior understanding of probability.
First up: Geometric and binomial probabilities
geometric probabilities:
Know the 4 characteristics that define a geometric distribution
Know how to find the expected value of x
Know how to find probabilities for values of x (both individual probabilities and cumulative probabilities)
bimomial probabilities:
geometric probabilities:
Know the 4 characteristics that define a binomial distribution
Know how to find the expected value of x
Know how to find probabilities for values of x (both individual probabilities and cumulative probabilities)
Be able to identify a binomial or geometric distribution when you read a problem.
Define the random variable x.
Solve problems related to probabilities for these distributions.
Next up: any other discrete distributions
Work with valid probability distributions (individual and cumulative)
Apply the concept of independent events to joint probability problems.
Apply the concepts of disjoint sets and complements to find probabilities.
Find the means and standard deviations of transformations of a random variable and combinations of independent random variables. YOu'll have to bookmark these pages and study them A LOT!
Monday December 6, 2010
Testing on Thursday on distributions of random variables. We will be learning new material through Wednesday. Be here!
We're combining parts of chapters 6-8 to build on students' prior understanding of probability.
First up: Geometric and binomial probabilities
geometric probabilities:
Know the 4 characteristics that define a geometric distribution
Know how to find the expected value of x
Know how to find probabilities for values of x (both individual probabilities and cumulative probabilities)
bimomial probabilities:
geometric probabilities:
Know the 4 characteristics that define a binomial distribution
Know how to find the expected value of x
Know how to find probabilities for values of x (both individual probabilities and cumulative probabilities)
Be able to identify a binomial or geometric distribution when you read a problem.
Define the random variable x.
Solve problems related to probabilities for these distributions.
Next up: any other discrete distributions
Work with valid probability distributions (individual and cumulative)
Apply the concept of independent events to joint probability problems.
Apply the concepts of disjoint sets and complements to find probabilities.
Find the means and standard deviations of transformations of a random variable and combinations of independent random variables. YOu'll have to bookmark these pages and study them A LOT!
Monday December 6, 2010
Testing on Thursday on distributions of random variables. We will be learning new material through Wednesday. Be here!
Thursday, November 04, 2010
Producing Data
So we've moved into survey design and experimental design. (Chapter 5 in the text.)
Important vocabulary:
Population
sample
census
bias
nonreaponse bias
undercoverage
response bias
convenience sample
stratified random sample
systematic random sample (like The Lottery by Shirley Jackson)
simple random sample (SRS)
We used the Table of Random Digits to (1) pick a sample, (2) Simulate a random event, and (3) randomly allocate participants to experimental treatments.
We have looked at a few experimental design/survey design questions from previous exams.
HW due Thursday 11/4: Problems 5.2, 5.3, 5.10 ,5.11
HW due Friday 11/5: Written answers on your own paper to the 1998 and 2002 experimental design questions handed out in class.
Important vocabulary:
Population
sample
census
bias
nonreaponse bias
undercoverage
response bias
convenience sample
stratified random sample
systematic random sample (like The Lottery by Shirley Jackson)
simple random sample (SRS)
We used the Table of Random Digits to (1) pick a sample, (2) Simulate a random event, and (3) randomly allocate participants to experimental treatments.
We have looked at a few experimental design/survey design questions from previous exams.
HW due Thursday 11/4: Problems 5.2, 5.3, 5.10 ,5.11
HW due Friday 11/5: Written answers on your own paper to the 1998 and 2002 experimental design questions handed out in class.
Friday, October 22, 2010
Bivariate distributions
We've moved from investigations using single variables to the world of two variables. The first type of bivariate relationship we study is the relationship between two numerical variables.
We collected data on Monday and crunched numbers again on Tuesday to find the least squares regression line and the coefficient of determination. R^2.
On Wednesday we studied the correlation coefficient, the slope and intercept of the LSRL, and the patterns in residuals. We saw that the point (x-bar, y-bar) lies on the LSRL and that R^2 may not be an indicator of a good model.
Based on your new knowledge of these concepts, please expand your 4 inch summary of section 3.1 to 5 inches of strong content.
Do the problems in section 3.1 that relate to the manatees and to the archaeopteryx.
Quiz answers:
scatterplot - points have a strong positive linear pattern with no outliers. Graph should have labels and scale.
LSRL y-hat = -10.64 + 4.117x
Residuals - y - y-hat graphed against x. To compute residuals, use L2 - Y1(L1). The graph shows that the residuals fluctuate above and below the axis with varying distances.
Interpretation - Because the residuals can be interpreted as randomly scattered about the residual = 0 line, the linear model is good.
Caveat- Because the residuals seem to be getting further from residuals = 0 as x gets larger, we might be concerned about our error increasing as length increases. Beware telescoping residuals.
October 8, 2010
This week student should have completed problems 3.35, 3.36, 3.37, & 3.37 from the text. For HW due Monday, they need to complete problems 3.39, 3.40, & 3.48.
What have we done so far? Collected bivariate data. Looked at them. Computed the LSRL. Computed residuals. Interpreted the residuals and the slope of the LSRL. Used the LSRL to predict a value of y. Performed a Linear regression t-test to determine the significance of the slope.
What do we have to do? Practice and interpret outputs.
ALSO, pick a book. Suggestions: A Civil Action, Freakonomics, Bringing Down the House, Moneyball, And the Band Played On, The Lady Tasting Tea. Get your parents' permission to read your book. You should have it finished by the end of Thanksgiving break.
Monday, October 11, 2010
We collected data that we expected to have no correlation. In 13 of the 15 cases, we got what we expected. We graphed the ordered pairs, computed the LSRL, checked the residuals, performed a linear regression t-test, and interpreted the results.
Small p-value>>> reject the null hypothesis--that there is no linear relationship between x and y. Instead, we have evidence indicating that there is a linear relationship.
Large p-value>>> fail to reject the null hypothesis. We do not have compelling evidence that there is a linear relationship.
HW problems 3.6 and 3.61
Have your papeback on Friday. You will be given a reading day.
_________________
As we continue through bivariate distributions, please take care to clearly identify the transformation you have performed on your lists in the calculator. For instance, log L2 may make sense to you, but you may be better off by renaming the list log life expectancy.
Typically, students have problems when they graph the curves through data. The linear regression graph only works with straightened (transformed) data. The curves go through the original data.
Your test on bivariate data will be Thursday, Oct 28.
We collected data on Monday and crunched numbers again on Tuesday to find the least squares regression line and the coefficient of determination. R^2.
On Wednesday we studied the correlation coefficient, the slope and intercept of the LSRL, and the patterns in residuals. We saw that the point (x-bar, y-bar) lies on the LSRL and that R^2 may not be an indicator of a good model.
Based on your new knowledge of these concepts, please expand your 4 inch summary of section 3.1 to 5 inches of strong content.
Do the problems in section 3.1 that relate to the manatees and to the archaeopteryx.
Quiz answers:
scatterplot - points have a strong positive linear pattern with no outliers. Graph should have labels and scale.
LSRL y-hat = -10.64 + 4.117x
Residuals - y - y-hat graphed against x. To compute residuals, use L2 - Y1(L1). The graph shows that the residuals fluctuate above and below the axis with varying distances.
Interpretation - Because the residuals can be interpreted as randomly scattered about the residual = 0 line, the linear model is good.
Caveat- Because the residuals seem to be getting further from residuals = 0 as x gets larger, we might be concerned about our error increasing as length increases. Beware telescoping residuals.
October 8, 2010
This week student should have completed problems 3.35, 3.36, 3.37, & 3.37 from the text. For HW due Monday, they need to complete problems 3.39, 3.40, & 3.48.
What have we done so far? Collected bivariate data. Looked at them. Computed the LSRL. Computed residuals. Interpreted the residuals and the slope of the LSRL. Used the LSRL to predict a value of y. Performed a Linear regression t-test to determine the significance of the slope.
What do we have to do? Practice and interpret outputs.
ALSO, pick a book. Suggestions: A Civil Action, Freakonomics, Bringing Down the House, Moneyball, And the Band Played On, The Lady Tasting Tea. Get your parents' permission to read your book. You should have it finished by the end of Thanksgiving break.
Monday, October 11, 2010
We collected data that we expected to have no correlation. In 13 of the 15 cases, we got what we expected. We graphed the ordered pairs, computed the LSRL, checked the residuals, performed a linear regression t-test, and interpreted the results.
Small p-value>>> reject the null hypothesis--that there is no linear relationship between x and y. Instead, we have evidence indicating that there is a linear relationship.
Large p-value>>> fail to reject the null hypothesis. We do not have compelling evidence that there is a linear relationship.
HW problems 3.6 and 3.61
Have your papeback on Friday. You will be given a reading day.
_________________
As we continue through bivariate distributions, please take care to clearly identify the transformation you have performed on your lists in the calculator. For instance, log L2 may make sense to you, but you may be better off by renaming the list log life expectancy.
Typically, students have problems when they graph the curves through data. The linear regression graph only works with straightened (transformed) data. The curves go through the original data.
Your test on bivariate data will be Thursday, Oct 28.
Monday, August 30, 2010
Measurements of position
Hmmm. Z values. Percentile ranks. Proportions between two x-values.
How are these connected for Normal distributions?
The percentile for a particular z-value is the value in the body of the Z table that represents the "sum" of the column and row titles. For Negative z-values, just append (attach) the hundredths place digit. For instance. . .
row 1.3, column 0.4 ==> 1.34 = z. This is the 90.99th percentile.
for row -2.3, column 0.4 ==> -2.34 = z. With a table value if 0.0096, this is just a hair under the 1st percentile.
The percentile is the proportion of data that lies to the left of the x value or is equal to it. If you took a test and scored at the 99th percentile, 99% of all other test scores should be equal to your score or below it.
Another way to find the percentile is to use the NormalCDF function on the calculator. Use NormalCDF(lower bound, upper bound) where the boundary values are z scores. To find the percentile for a Normally-distributed z value, we use the lower bound of negative infinity and the upper bound of the z under consideration.
We can use -999999 for negative infinity. NormalCDF(-999999,1) = the proportion of the population of Normally distributed z values that fall equal to or below 1.
To find the Z value for a particular percentile, use the inverse of the NormalCDF function-- INVNorm. To find the 95th percentile, enter InvNorm(.95). Approximately 95% of all z-values in a Normal distribution will fall below this value.
To find the X value that corresponds to the desired Z value, take the mean and add Z standard deviations.
Practice converting X values into z values adn percentiles into X values. Do the problems on page 147.
How are these connected for Normal distributions?
The percentile for a particular z-value is the value in the body of the Z table that represents the "sum" of the column and row titles. For Negative z-values, just append (attach) the hundredths place digit. For instance. . .
row 1.3, column 0.4 ==> 1.34 = z. This is the 90.99th percentile.
for row -2.3, column 0.4 ==> -2.34 = z. With a table value if 0.0096, this is just a hair under the 1st percentile.
The percentile is the proportion of data that lies to the left of the x value or is equal to it. If you took a test and scored at the 99th percentile, 99% of all other test scores should be equal to your score or below it.
Another way to find the percentile is to use the NormalCDF function on the calculator. Use NormalCDF(lower bound, upper bound) where the boundary values are z scores. To find the percentile for a Normally-distributed z value, we use the lower bound of negative infinity and the upper bound of the z under consideration.
We can use -999999 for negative infinity. NormalCDF(-999999,1) = the proportion of the population of Normally distributed z values that fall equal to or below 1.
To find the Z value for a particular percentile, use the inverse of the NormalCDF function-- INVNorm. To find the 95th percentile, enter InvNorm(.95). Approximately 95% of all z-values in a Normal distribution will fall below this value.
To find the X value that corresponds to the desired Z value, take the mean and add Z standard deviations.
Practice converting X values into z values adn percentiles into X values. Do the problems on page 147.
Friday, August 20, 2010
New data!!!! Haircut costs
As we learn to represent and interpret our data, we collected the following data:
boys' haircut prices
12, 18, 22, 0, 0 ,0, 15, 0, 17, 16, 17.95, 10, 12
girls' haircut prices
35, 55, 50, 30, 18, 25, 0, 50, 40, 45, 45, 140, 40, 8, 25, 30, 22, 28
Represent each of these as a boxplot on the same axes AND
using the information starting on page 42 in the text, represent it also as a back to back stemplot.
We will interpret your results on Tuesday.
Be safe.
_________________________
8/20
We've used histograms, boxplots, and stemplots to represent univariate (one-dimensional) data. We've worked many problems from previous AP exams.
You're probably ready to close out this chapter (1). Let's focus on the parts we haven't covered so far and test on Thursday, 8/26.
We will start the CiCi's Sundays on August 29, unless you do not need help yet.
Be safe. Play hard. Go Trojans.
boys' haircut prices
12, 18, 22, 0, 0 ,0, 15, 0, 17, 16, 17.95, 10, 12
girls' haircut prices
35, 55, 50, 30, 18, 25, 0, 50, 40, 45, 45, 140, 40, 8, 25, 30, 22, 28
Represent each of these as a boxplot on the same axes AND
using the information starting on page 42 in the text, represent it also as a back to back stemplot.
We will interpret your results on Tuesday.
Be safe.
_________________________
8/20
We've used histograms, boxplots, and stemplots to represent univariate (one-dimensional) data. We've worked many problems from previous AP exams.
You're probably ready to close out this chapter (1). Let's focus on the parts we haven't covered so far and test on Thursday, 8/26.
We will start the CiCi's Sundays on August 29, unless you do not need help yet.
Be safe. Play hard. Go Trojans.
Monday, May 10, 2010
Gearing up for the final exam
So far we've discussed good answers for problems 1-4 of the operational exam. The take-home part of your final will be one of the 6 questions, randomly selected two days before your exam. Get to work developing your best answers to these questions.
The in-class part of the final exam will be cumulative, with an emphasis on second semester topics.
Random assignment of problems for take-home portion:
6th period seniors: #3 YOU MAY NOT COLLABORATE ON THIS PROBLEM NOW THAT IT HAS BEEN ASSIGNED. THE WORK YOU TURN IN MUST BE YOUR OWN.
The in-class part of the final exam will be cumulative, with an emphasis on second semester topics.
Random assignment of problems for take-home portion:
6th period seniors: #3 YOU MAY NOT COLLABORATE ON THIS PROBLEM NOW THAT IT HAS BEEN ASSIGNED. THE WORK YOU TURN IN MUST BE YOUR OWN.
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