AP Statistics

calculator dictionary graph paper graph simulator


Statistics online help - Pearson Education

        In the drop down menu pick pick the following category:
        sullivan: statistics: informed decisions using data, 3e


AP Statistics - Fall 2011; unit 1,2,3,4,5,6,7,8,9,10,11

       AP Statistics - syllabus
       AP Statistics - formula packet


Useful Stats links - refer to these regularly to help 'get it'!


        60 minutes - Statistics used to catch cheaters in poker

        another CLT (Central Limit Theorem)applet

        AP Central Test Schedule & Fees

        Central Limit Theorem practice website (sampling distribution)

        chi-squared link - drexel question blog

        correlation by eye applet

        drexel forum on chi-squared test

        Random.org - introduction to randomness

        Random Variables vs. Algebraic Variables

        Regression applet

        Regression by eye applet

        Type I & Type II errors - The link for the applet is at the bottom of the page.

        Confidence intervals - Option 2 is good. Choose a confidence level and click animate. Watch as you see the selection of samples and the corresponding confidence intervals for the selected samples. For each you can see if the population parameter falls within the interval.

        Why Variance Matters - Ap Central


BVD Stats tutorials - Pearson

        01. Stats Starts Here
        02. Data
        03. For Example: Identifying the Who What and Why
        04. Displaying and Describing Categorical Data
        05. Step-by-Step Example: Examining Contingency Tables
        06. Displaying and Summarizing Quantitative Data
        07. Step-by Step Example: Shape, Center, and Spread
        08. Step-by-Step Example: Summarizing a distribution
        09. Understanding and comparing Distributions
        10. Step-by-Step Example: Comparing Groups
        11. The Standard Deviation as a Ruler
        12. Step-by-Step Example: Working with Standardized Variables
        13. Step-by-Step Example: Working with the 68-95-99.7 rule
        14. Step-by-Step Example: Working with Normal Models I
        15. Step-by-Step Example: Working with Normal Models II
        16. Step-by-Step Example: More working with Normal Models
        17. Scatterplots, Association and Correlation
        18. Step-by-Step Example: Looking at Association
        19. Linear Regression
        20. Step-by-Step Example: Calculating a Regresion Equation
        21. Step-by-Step Example: Regression
        22. Regression Wisdom
        23. For Example: Using Several of These Methods Together
        24. Re-expressing Data: Get It Straight!
        25. Step-by-Step Example: Re-expressing to Straighten a Scatterplot
        26. Understanding Randomness
        27. Step-by-Step Example: Simulation
        28. Sample Surveys
        29. Step-by-Step Example: Sampling
        30. Experiments and Obervational Studies
        31. Step-by-Step Example: Designing an Experiment
        32. From Randomness to Probability
        33. Step-by-Step Example: Probability
        34. Probability Rules!
        35. Step-by-Step Example: Using the General Addition Rule
        36. Step-by-Step Example: Are the Events Disjoint? Independent?
        37. Step-by-Step Example: Reversing the Condition
        38. Random Variables
        39. Step-by-Step Example: Expected Values and Standard Deviation of Discrete Random Variables
        40. Step-by-Step Example: Hitting the Road: Means and Variances
        41. Step-by-Step Example: Packaging Stereos
        42. Probability Models
        43. Step-by-Step Example: Working with a Geometric Model
        44. Step-by-Step Example: Working with the Binomial Model
        45. Sampling Distribution Models
        46. Step-by-Step Example: Working with Sampling Distrubution Models for Proportions
        48. Step-by-Step Example: Working with the Sampling Distribution Model for the Mean
        49. Confidence Intervals for Proportions
        50. Step-by-Step Example: A confidence Interval for a Proportion
        51. Testing Hypotheses about Proportions
        52. Step-by-Step Example: Testing a Hypothesis
        53. Step-by-Step Example: Tests and Intervals
        54. More About Tests and Intervals
        55. Step-by-Step example: Another One-Proportion Z-test         56. Step-by-Step Example: Wear that Seatbelt!
        57. Comparing Two Proportions
        58. Step-by-Step Example: A Two-Proportion z-Interval
        59. Step-by-Step Example: A Two-Proportion z-test
        60. Inferences About Means
        61. Step-by-Step Example: A One-Sample t-interval for the Mean
        62. Step-by-Step Example: A One-Sample t-Test for the Mean
        63. Comparing Means
        64. Step-by-Step Example: A Two-Sample t-Interval
        65. Step-by-Step Example: A Two-Sample t-Test for the Difference Between Two Means
        66. Paired Samples and Blocks
        67. Step-by-Step Example: A Paired t-Test
        68. Step-by-Step Example: A Paired t-Interval
        70. Comparing Counts
        71. Step-by-Step Example: A Chi-Square Test for Goodness of Fit
        72. Step-by-Step Example: A Chi-Square TEst for Homogeneity
        73. Step-by-Step Example: A Chi-Square Test for Independence
        74. Inference for Regression
        75. Step-by-Step Example: Regression Inference
        76. Step-by-Step Example: A Regression Slope t-test


Unit 1 - Univariate Data Analysis


        AP Statistics - unit 1 checklist

        AP Statistics - unit 1 learning targets

        AP Statistics - unit 1 lesson 1-2

        AP Statistics - unit 1 lesson 1-3

        AP Statistics - unit 1 lesson 1-4

        AP Statistics - unit 1 lesson 1-5

        AP Statistics - unit 1 lesson 1-6

        AP Statistics - unit 1 lesson 1-7

        AP Statistics - unit 1 lesson 1-8

        AP Statistics - unit 1 lesson 1-10

        AP Statistics - unit 1 lesson 1-11

        AP Statistics - unit 1 lesson 1-12

        AP Statistics - unit 1 lesson 1-13

        AP Statistics - unit 1 lesson 1-14


        chapter 3 cheat sheet

Unit 2 - Bivariate Data Analysis


        AP Statistics - unit 2 supplemental reading (30 pages may take a moment to load)

        AP Statistics - unit 2 checklist

        AP Statistics - unit 2 learning targets

        AP Statistics - unit 1 lesson 2-1

        AP Statistics - unit 1 lesson 2-2

        AP Statistics - unit 1 lesson 2-3

        AP Statistics - unit 1 lesson 2-4

        AP Statistics - unit 1 lesson 2-5

        AP Statistics - unit 1 lesson 2-6

        AP Statistics - unit 1 lesson 2-7

        AP Statistics - unit 1 lesson 2-8

        AP Statistics - unit 1 lesson 2-9

        AP Statistics - unit 1 lesson 2-10


Unit 3 - Planning Studies & Experiments


        AP Statistics - unit 3 supplemental reading (22 pages may take a moment to load)

        AP Statistics - unit 3 checklist

        AP Statistics - unit 3 learning targets

        AP Statistics - unit 3 lesson 3-1

        AP Statistics - unit 3 lesson 3-2

        AP Statistics - unit 3 lesson 3-3

        AP Statistics - unit 3 lesson 3-4

        AP Statistics - unit 3 lesson 3-6

        AP Statistics - unit 3 lesson 3-7

        AP Statistics - unit 3 lesson 3-8

        AP Statistics - unit 3 lesson 3-9

        AP Statistics - unit 3 lesson 3-10

        AP Statistics - unit 3 lesson 3-11


Unit 4 - Probability


        AP Statistics - unit 4 supplemental reading (22 pages may take a moment to load)

        AP Statistics - unit 4 checklist

        AP Statistics - unit 4 learning targets

        AP Statistics - unit 4 lesson 4-41

        AP Statistics - unit 4 lesson 4-2

        AP Statistics - unit 4 lesson 4-3

        AP Statistics - unit 4 lesson 4-4

        AP Statistics - unit 4 lesson 4-5

        AP Statistics - unit 4 lesson 4-6

        AP Statistics - unit 4 lesson 4-7


Unit 5 - Binomial & Geometric Distributions


        AP Statistics - unit 5 learning targets

        AP Statistics - unit 5 lesson 5-1

        AP Statistics - unit 5 lesson 5-2

        AP Statistics - unit 5 lesson 5-3

        AP Statistics - unit 5 lesson 5-4

        AP Statistics - unit 5 lesson 5-5

        AP Statistics - unit 5 lesson 5-6

        AP Statistics - unit 5 lesson 5-7


Unit 6 - Random Variables & Sampling Distr


        AP Statistics - unit 6 learning targets

        AP Statistics - unit 6 lesson 6-1

        AP Statistics - unit 6 lesson 6-2

        AP Statistics - unit 6 lesson 6-3

        AP Statistics - unit 6 lesson 6-4

        AP Statistics - unit 6 lesson 6-5

        AP Statistics - unit 6 lesson 6-6

        AP Statistics - unit 6 lesson 6-7

        AP Statistics - unit 6 lesson 6-8

        AP Statistics - unit 6 lesson 6-9


Unit 7 - Intro to Inference


        AP Statistics - unit 7 learning targets

        AP Statistics - unit 7 lesson 7-1

        AP Statistics - unit 7 lesson 7-2

        AP Statistics - unit 7 lesson 7-3

        AP Statistics - unit 7 lesson 7-4

        AP Statistics - unit 7 lesson 7-5

        AP Statistics - unit 7 lesson 7-6

        AP Statistics - unit 7 lesson 7-7

        AP Statistics - unit 7 lesson 7-8

        AP Statistics - unit 7 lesson 7-9


Unit 8 - Inference for Means


        AP Statistics - unit 8 learning targets

        AP Statistics - unit 8 lesson 8-1

        AP Statistics - unit 8 lesson 8-2

        AP Statistics - unit 8 lesson 8-3

        AP Statistics - unit 8 lesson 8-4

        AP Statistics - unit 8 lesson 8-5

        AP Statistics - unit 8 lesson 8-6

        AP Statistics - unit 8 lesson 8-7


Unit 9 - Inference for Proportions


        AP Statistics - unit 9 learning targets

Lesson Objectives:

What proportion of m&m candies are yellow?
Learn how to properly construct confidence intervals for proportions. This will be in part a review of the proportion content from Unit 7.

Confidence intervals for proportions:
Visit the Hyperstat site to learn about setting up confidence intervals for proportions. Be sure to only work through the 3 pages on this topic.


        AP Statistics - confidence intervals


        AP Statistics - confidence intervals powerpoint

        AP Statistics - unit 9 lesson 9-1

Conclusion:

You should now know how to construct and correctly interpret confidence intervals for a proportion. Be sure to be precise with your terminology. Be sure to complete:
?assignment 9.1
The next lesson focuses on significance testing for one proportion.

Lesson Objectives:

15% of peanut m&ms are supposed to be yellow. Is the proportion of yellows from a sample good evidence that the proportion isn't really 15%?
Learn how to conduct significance tests for a proportion.

Significance test tutorial:
Practice setting up and conducting hypothesis tests for proportions. If you need additional review for conducting tests, follow the link:
Information on conducting a hypothesis test for a proportion at the bottom of the page.

        AP Statistics - significance tutorial

Significance Testing with one proportion:

Visit the Hyperstat site to learn about what significance testing looks like when dealing with one proportion. Be sure to only work through the 4 pages on this topic.

        AP Statistics - significance testing

        AP Statistics - significance testing powerpoint

        AP Statistics - unit 9 lesson 9-2

Conclusion:

You should now be a pro at conducting significance tests with a proportion. Don't forget the conditions! Be sure you have completed:
?assignment 9.2
The next lesson focuses on the use of your calculator to aid in confidence intervals and tests as well as how to determine the sample size needed for a given margin of error.

Lesson Objectives:

How large a sample would be necessary to determine if there is a home court advantage in college basketball?
Learn how to determine sample size for working with proportions. Also refine your calculator skills in review of confidence intervals and tests.

Using the Calculator to find Confidence Intervals:
See a tutorial on using the TI-83/84 calculator to construct confidence intervals.

        AP Statistics - calculating a confidence interval

Using your calculator to run one proportion z-tests:
Be sure you can correctly interpret the calculator output.

        AP Statistics - proportion z-test

        AP Statistics - sample size powerpoint

Additional look at using your calculator:
See examples from both the 83/84 and the 89!

        AP Statistics - more calculator help!

        AP Statistics - unit 9 lesson 9-3

Conclusion:

You should now be able to determine a minimal sample size as well as being very efficient using your calculator to construct
one proportion confidence intervals and conduct one proportion significance tests. Be sure you have completed:
?assignment 9.3
?quiz 9a
The next lesson focuses on constructing confidence intervals for comparing two sample proportions.

Lesson objectives:

Is there a difference between the proportion of women who vote and the proportion of men who vote?
Learn to construct two proportion confidence intervals in order to compare proportions. Also learn to use your calculator to construct these.

Confidence intervals for 2 proportions:

Go to the Hyperstat site to learn about confidence intervals for 2 proportions. Be sure to only work through the 4 pages on this topic.


        AP Statistics - confidence intervals supplemental reading


        AP Statistics - confidence intervals powerpoint


        AP Statistics - confidence intervals calculator test


        AP Statistics - unit 9 lesson 9-4

Conclusion:

You should now be able to construct two proportion confidence intervals by hand as well as by using the calculator. Always remember to show how you check assumptions! Be sure to complete: ?assignment 9.4
The next lesson focuses on significance tests for two proportions.

Lesson Objectives:

Is there a difference between the proportion of workers who believe in e-mail monitoring and the proportion of bosses who believe in e-mail monitoring?
Learn to conduct two proportion significance tests. As the calculations become more intense, we will rely on the calculator to do the arithmetic

Significance testing for two proportions:

Visit the Hyperstat site to experience the significance test for the difference between two proportions. Be sure to only work through the 5 pages on this topic.

        AP Statistics - testing of proportions

        AP Statistics - testing of proportions powerpoint

        AP Statistics - unit 9 lesson 9-5

Conclusion:

You should now be able to successfully conduct a two proportion z test of significance. Be sure to check assumptions (conditions), report calculations, and write conclusions.
Be sure you have completed:
?assignment 9.5
The next lesson includes review and the Unit 9 test.

        AP Statistics - unit 9 lesson 9-6


Unit 10 - Inference for Categorical Variables


        AP Statistics - unit 10 learning targets

Lesson 10.1 - Chi-Squared Test for Goodness of Fit:

Learn how to test many proportions at once instead of just one or two! That is, instead of just wondering if you got the "right" amount of yellow m&ms in your bag,
determine if the entire bag is "right."
This lesson should take approximately 1.5 hours.

Introduction:

They're Back! How can I determine if not just my yellows but my whole bag of m&ms is not right (in terms of color)?
Learn to conduct a chi-squared Goodness of Fit Test to test a group of proportions.

Overview of the Goodness of Fit Test:
Once you understand the general idea and purpose of the Goodness of Fit test, this site provides a good overview and a couple of worked examples.

        AP Statistics - goodness of fit supplemental reading

The Goodness of Fit Test:

See a good explanation of how the goodness of fit test can test several proportions of a single variable in one test.
It's like doing a 4-proportion z-test or a 5-proportion z-test or an x-proportion z-test!

        AP Statistics - goodness of fit tutorial

        AP Statistics - goodness of fit powerpoint

        AP Statistics - unit 10 lesson 10-1

Conclusion:


You should now be able to conduct a chi-squared test for goodness of fit.
Recall that this is a convenient test to determine if a sampled series of proportions is "as advertised" or as expected. Be sure you have completed:
?assignment 10.1
The next lesson focuses on checking the conditions under which the goodness of fit test may be performed as well as the role of the calculator in the test.

Lesson 10.2 - Goodness of Fit Conditions and the Calculator:

Discover the conditions or assumptions under which we may perform the Goodness of Fit test. Also, learn the calculator's role.
Those of you with a TI-89 are at a bit of an advantage (for a change) with the Goodness of Fit test. A quiz is included in this lesson.
This lesson should take approximately 2.5 hours.


Introduction:
How can I tell if a 6-sided die is fair (and not loaded) - I think my friend has been cheating at Yahtzee!
Use a large sample (so you meet the conditions/assumptions) and the Goodness of Fit test to find out!

        AP Statistics - goodness of fit conditions

Great video tutorials here for chi-square understanding!

        AP Statistics - goodness of fit conditions

Ti 89 Calculator Help:

This site may provide some additiuonal help for ti-89 calculator users.
In a nutshell, to perform a chi-squared Goodness of Fit Test, Enter your observed and expected counts into lists and then simply go to tests and choose chi-squared GOF.
The rest should be relatively intuitive.

        AP Statistics - statistics with a TI-89

        AP Statistics - unit 10 lesson 10-2

Conclusion:

You should now be an expert in conducting the goodness of fit test.
Remember to name the test, check assumptions/conditions, state hypotheses, show calculations, and draw statistical and contextual conclusions.
Be sure you have completed:
?assignment 10.2
?quiz 10a
The next lesson works with a different type of chi-squared test, the test of association or independence.

Lesson 10.3 - Chi-Squared Test of Association / Independence:

What's one more test at this point? Use chi-square to determine if there is an association or independence between two categorical variables.
This lesson should take approximately 1.5 hours.


Introduction:

Did the upper class people on the Titanic really survive at a different rate than the lower class people?
Learn to use the chi-square Test of Independence to determine if there really was a connection between socioeconomic status and survival rate.


This links to a program that performs the test of independence for you. It's pretty slick, just enter in data from a table and it does all
the calculations and provides you with the test statistic and p-value.
You start by entering in the number of rows and columns and then the data. Check it out and even use it to complete the assignment.


        AP Statistics - make a chi-square worksheet


Overview of Test for Independence:

Once you understand the basics, this is a good overview of the chi-squared test of independence and also includes worked examples.
Don't worry about the second example which refers to a textbook.


        AP Statistics - test for indendence


        AP Statistics - test for independence powerpoint


        AP Statistics - unit 10 lesson 10-3


Conclusion:

You should now be able to examine a two-way table showing the relationship between categorical variables and determine whether the variables are independent of not.
Be sure you have completed:
?assignment 10.3
The next lesson really streamline the chi-squared test of independence through the use of the calculator.

Lesson 10.4 - Chi-Squared Test of Independence: Conditions and the Calculator:

Understand the conditions for the test of independence. Also learn to let your calculator do an immense amount of the work for you as you conduct tests of independence.
This lesson should take approximately 1.5 hours.


Introduction:
Obtain extra practice with the test of independence.

        AP Statistics - chi-square tests


Conclusion:

You should now be an expert in conducting both chi-squared tests; goodness of fit and test of independence.
The calculator plays a neary indispensable role, be sure you are competent and confident. Be sure you have completed:
?assignment 10.4
The next lesson is a bit of review and the unit 9 test.

        AP Statistics - unit 10 lesson 10-4


Unit 11 - Inference for Regression



        AP Statistics - unit 11 learning targets


Conditions for Regression Inference:
Before you may conduct inference, you must meet certain conditions (or make assumptions).
This is no different than it was for t, z, or chi-squared. Here are the conditions for regression:
First, remeber that we have n observations (that is, n data points) of an explanatory variable x and a response variable y.
In order to conduct the inference:
?For any value of x, the response variable y varies according to a normal distribution and are independent.
?The mean response of y has a straight line relationship with x. That is the mean y = a + bx. Remember the slope b and intercept a are unknown.
?The standard deviation of y is the same for all values of x and is unknown.

We will discuss how to state these conditions later.

Work through this tutorial to get a sense of how we may construct a confidence interval for the slope of a regression line.

        AP Statistics - regression line inference


Summary:
To keep it simple, a confidence interval for the slope is not much different than all the other intervals you have created.
You have a mean slope (calculated from the regression) and you create your interval around it. Since it is a mean, you use t.
One difference is you use n-2 degrees of freedom to find t*. This t* is then mulitplied (just like before) the standard error
(which is typically given to you in the computer output).


        AP Statistics - unit 11 lesson 11-1


Work through this tutorial to get an idea of how to test for slope:

        AP Statistics - testing for slope
Summary:
The big idea of hypothesis testing is quite similar to that of chi-square testing for independence.
?We assume there is no relationship by stating that the slope is 0 (our null hypothesis).
We then suspect (alternate hypothesis) that there is a relationship by stating that the slope is not equal to 0.
?For your calculations, your test statistic is a t which is simply the slope found by regression divided by the standard error.
For the p-value, remember to use n-2 degrees of freedom.
?Conclusions are the same as we have done before.
One advantage is that your TI calculators have a built in test for this called LinRegtTest for which
you only need to input your data (from lists) and your alternate hypothesis.


        AP Statistics - unit 11 lesson 11-2

        AP Statistics - unit 11 review notes


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