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## Chapter 9 - Day 12

##### Questions to be Sure to Include
• A multiple choice question that gives four different ways of calculating the z-test statistic for a test for a proportion.

• A multiple choice question where students have to identify the possible ways of increasing the power of a test.

• On the free response, you should have two questions. One question asking students to do a significance test for a proportion, and one question asking students to do a significance test. Use old AP questions.

• Consider having a follow up question part (b) for each significance test. Here are some options for your follow-up question:

• Given your conclusion in part (a), which kind of mistake—a Type I error or a Type II error—could you have made? Explain what this mistake would mean in context.

• Why do we check the (random, 10%, Large Counts) condition?

• A simulation based estimate of the P-value (seriously 2009B #5 is the best question ever….if your students do well on this question, then you did a great job teaching Chapter 9!)

• Give students the confidence interval for the data in part (a) and ask them to explain why the confidence interval leads to the same conclusion as the significance test.

• Ask students if the significance test reveals a causal relationship. If the data comes from an observational study, then we cannot infer causation.

• The power of this test to detect the alternative (Ha) is _______. Interpret this value.

##### Tips to Give Your Students
• Close reading and careful writing are critical to your success this year.

• Be sure to answer all parts of each question.

• There are a lot of formulas in this Chapter. Don’t memorize them.  Understand them. Use the (general formula, specific formula, plug numbers in, find answer) approach.

• When reading a free response question, ask yourself “Is this context about a proportion or about a mean”. Your notation, conditions, and formulas depend on the answer to this question. Pro tip: variables that are categorical can be measured in proportions and variables that are quantitative can be measured with means.

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