Part II – Analyzing Data 1. Exploring Data 19 2. Describing Location in a Distribution 27 3. Examining Relationships 35 Part III – Probability and Random Variables 5. Probability: What Are the Chances? 43 6. Random Variables 47 7. Sampling Distributions 55 Part IV - Inference 8. Estimating with Confidence 59 9. Testing a Claim 65 10. Comparing Two Populations or Groups 71 11. Inference for Distributions of Categorical Data 77 12. More about Regression 83 Appendices Appendix A – Portfolio Information 89 Appendix B – Formulas and Tables 91 Appendix C – Inference Summary 97 I. Course Introduction Background. An understanding of statistics is necessary for anyone to be a savvy consumer, an informed citizen of a democracy, and a successful student of many other disciplines. The AP Statistics course gives students an opportunity to build a deep conceptual understanding of graphical analysis and statistical inference and the roles they play in decision making. Advanced Placement Course. This is a class that will move at a very fast pace. Students who take this course are assumed to be: (1) capable of working at the college level, and (2) willing to work at the college level. If you do not feel you meet these two requisites, I highly encourage you to change your schedule. There is a reason that extra GPA quality points are awarded for Advanced Placement classes. That having be said, if your reason for taking this course is to enhance your GPA, you have come to the wrong place with the wrong instructor. In order to receive AP credit for this course, students must take the Advanced Placement Examination which will be administered on Thursday, May 17 at 12 noon. How to Succeed in Mr. Mayo’s AP Statistics Class. Years ago as an AP Calculus teacher, I put together the following advice to my students concerning how to approach the course. (If you have recently taken
5. Explain how undercoverage, nonresponse, and question wording can lead to bias in a sample survey? 6. Distinguish between an observational study and an experiment? 7. Explain how unknown variables in an observational study can lead to confounding? 8. Identify the experimental or subjects, explanatory variables (factors), treatments, and response variables in an experiment? 9. Describe a completely randomized design for an experiment? 10. Explain why random assignment is an important experimental design principle? 11. Describe how to the placebo effect in an experiment? 12. Explain the meaning and the purpose of blinding in an experiment? 13. Explain in context what “statistically significant” means? 14. Distinguish between a completely randomized design and a randomized block design? 15. Know when a matched pairs experimental design is appropriate and how to implement such a design? 16. Determine the scope of inference for a statistical study? 17. Evaluate whether a statistical study has been carried out in an ethical manner? Technology Random number generation Press [MATH] <PRB> 5:randInt( Complete the entry on 5:randint( with the lowest integer value, highest integer value, and number of digits you want. [ENTER] and the numbers will be produced. Numbers can also be produced and stored in a list by using the [STO>] key Chapter 1 – Exploring Data
A. Estimation estimators and confidence intervals) (10.1, 10.2) 5. Large sample confidence interval for a difference between two proportions 7. Confidence interval for a difference between two means (unpaired and paired) B. Tests of significance (10.1, 10.2) 3. Large sample test for a difference between two proportions 5. Test for a difference between two means (unpaired and paired) Key Vocabulary Inference about proportions Two-sample z interval for p1-p2 (2-PropZInt) An approximate level C confidence interval for is z* is the standard Normal critical value. Random: The data are producd by a random sample of size n1 from population 1 and a random sample of size n2 from population 2 or by two groups of size n1 and n2 in a randomized experiment. Normal: The counts of “successes” and “failures” in each sample or -- n1p1, n1(1-p1), n2p2, – are at least 10. Independent: Both the samples or groups themselves and the individual observations in each sample or group are independent. When sampling without replacement, check that the two populations are at least 10 times as large as the corresponding samples (the 10% condition). Test Two-sample z test for p1-p2 (2-PropZTest) Significance tests of H0: p1 – p2 = 0 use the pooled (combined) sample proportion The two-sample z test for p1-p2 uses the test statistic with P-values calculated from the standard Normal distribution. Random: The data are producd by a random sample of size n1 from population 1 and a random sample of size n2 from population 2 or by two groups of size n1 and n2 in a randomized experiment. Normal: The counts of “successes” and “failures” in each sample or group -- n1p1, n1(1-p1), n2p2, n2(1-p2) – are at least 10. Independent: Observations and independent samples or groups; 10% condition if sampling without replacement
Technology 1. Checking conditions for linear regression After performing linear regression, plot residuals as detailed in Chapter 3. Check to confirm sum of residuals is 0. Another way to do this is to use the SUM( command and the variable RESID. Type [2nd] [STAT] (LIST) <MATH> 5:SUM( [ENTER] and then type [2nd] [STAT] (LIST) <NAMES> and choose RESID and [ENTER] 2. Linear regression t-test Enter data intonL1 and L2. Press [STAT] <TESTS> F:LinRegTTest Press [ENTER] In the LinRegTTest screen, specify L1 for Xlist and L2 for Ylist and ≠0 for the hypothesized slope. Highlight the command Calculate and press [ENTER]. The linear regression t test results take two screens to present Modeling exponential growth Enter the exponential data into L1 and L2. Plot shows exponential growth Define L3 as the natural logarithm of L2. Make a scatterplot of L1 and L3. Perform regression on the transformed data and graph the plot again with the regression line. Construct and inspect the residual plot. To use the model to predict, define Y2 = e^(Y1) then enter x-values in Y2( ) and [ENTER]. For example, to predict a for an x of 33, enter Y2(33).