ap statistics homework help

ap statistics homework help

Advanced Techniques for AP Statistics Homework Success

1. Introduction to AP Statistics

The Advanced Placement (AP) program offers a high school statistics course designed to prepare students for college-level statistics coursework. A skills-based course, AP Statistics prepares students to apply data collection, organization, analysis, and drawing of inferences to real-world problems. In the fall of the traditional high school statistics course, students familiarize themselves with the basic practice of statistics. Key course goals include articulation of results of statistical analysis. Among other concepts, units include critical value analysis, hypothesis testing, and confidence intervals. Descriptive statistics, bias, and post hoc testing are also studied. A normal model, simulation, random sampling, and random sampling distributions are also discussed. While it is true that a student could gain a basic understanding of these concepts from a traditional introduction to statistics course, the AP course delves a little deeper into the details.

Introduction to Advanced Placement (AP) Statistics

2. Key Concepts and Formulas

E(µ) = µ; E(x ± µ) = E(x) ± µ; E(x ± y ± z ± ···) = E(x) ± E(y) E(-x) = -E(x); E(kx) = kE(x); k and C are constants; E(x + y) = E(x) + E(y) only if x and y are independent. Var(µ) = 0; Var(x) = Var(-x) = Var(xx); Var(x ± µ) = Var(x); Var(xx + xy) = Var(xx) + 2Cov(xx,xy) + Var(xz) Generally, the notation E(X) is used to represent the mean or expected value of the random variable X. Likewise, the notation Var(X) or σ²x is used to represent the variance of X and σx is used to denote its standard deviation. Other features of these key concepts are as follows. E(x) = µxb; Var(x) = µxxb – µ²x; • E(a+bx) = a+bE(x); • Var(a+bx) = b²Var(x)

Listed below are the main concepts that all AP Statistics students need to know. These concepts are all testable, and the corresponding topics are not only specific anchor points but also ones that the test writers have used over the years time and time again. For many students, the terms are new and the meaning unintuitive. Therefore, it is important to memorize the definitions and to repeat them as often as possible in different contexts.

3. Problem-Solving Strategies

If you have found this advice useful but don’t remember some of the details, write down brief notes on such advice sheets and keep them in your notebook or textbook. Try to study these in the evenings for a few evenings on several consecutive weeks. Over the course of a few weeks, these habits will become automatic, and, like Rick in the first story, you can find unexpected problems where previous students have found only ho-hum questions.

Draw a diagram. A diagram can help you visualize the problem. Is there some symmetry that will simplify matters? Are division or approximation relationships useful?

Consider special cases. Sometimes it helps to consider a solution in the context of particular data, even if they are just made up under the constraints of the problem. The conditions given may not be particularly well suited for the problem at hand.

Analyze the problem. Try changing the perspective of the problem—do you see the problem in a new light? Try a simpler version of the problem. Could a table, list, graph, tree diagram, or flow chart help? Could averaging or proportional reasoning be applied?

Check your understanding. Ask yourself what the problem requires and what is known. Are there any restrictions on the unknown or on data given in the problem?

As you work on your AP Statistics homework (and on other problems as well), here are some strategies you might find useful:

4. Practice Problems and Quizzes

The quizzes are skills-based. That is, they ask the student to apply knowledge he or she has learned in the text in a way that is less contrived than the typical “Chances Are” problems in the text itself. The problem sets in the chapter are problem-type based and are similar in evolution to these quizzes. Each quiz is designed to emphasize the new material in the two sections leading up to it. So when students take the quiz in class, they’ve learned the skills necessary during two to three days filled with textbook work, case studies, and classes. Each quiz is given the night before the students are given the answer key to the chapter’s exercise sets. Thus students have an opportunity to work problems in the absence of an answer key and to compare their answers with the key the next day.

AP Statistics students will find both written problems and quizzes throughout the textbook at just the right spacing to help gauge student understanding and promote understanding. The written problems help students understand key concepts, whereas the quizzes lead to mastery of the concepts. The problems in the book may also be used as computer-based practice problems or quizzes using the book website.

5. Conclusion and Further Resources

Mason, Robert L. and Greene, Donald S. (1993). “Statistics for Technology”, and Hawthorne, Orrin M. Jr. (1988). “Applied Management Science – Modeling, Spreadsheet Analysis, and Communication for Decision Making”.

Aside from “Elements of Fifth Edition (2005)”, other excellent references include:

Quando operare – Graphical solution to the EOQ with quantity/discount/time tradeoff.

Properties of Z and Percent Efficient Control Charts for Short Lots. Technical Report No. 249, November 1994, Updated May 2006.

Advance in one direction to other designs: leverage control chart methods for more advanced sampling techniques. Advance in another direction to special applications such as ranked m-regulation, multivariate, variable, or zero acceptance number attributes control charts, including even mini-max designs large enough to say your process, product, or employees meeting minimum or even no defects goals.

Further Study in the Control Charts Area

As always, it’s amazing when we see just how valuable the final insights in a study can be. For instance, once you have summarized the major findings of a study (my new arbitrary measure of the importance of the findings), you may use control charts to monitor and improve the quality of a process. Even when the quality of a process is just barely adequate, use process control to stabilize your process so it delivers consistent planned results. If a process is underperforming, instead of aggressive adjustment, follow the method of rational sub-grouping. Be aware that with learning curves or plan-attend-review-educate, reading and learning, catch up may take many hours. These hour-by-hour investments are crucial to successfully use the most advanced, powerful, and fundamental concepts in the AP Statistics syllabus.

Conclusion of Lesson 5