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9.2 Hypothesis Testing for Proportions

For purposes of the AP exam, there are four major parts to a hypothesis test:

I. States a correct pair of hypotheses—this includes:

• Describing the variable—the population parameter of interest

• Null hypothesis—a statement that the parameter takes a particular value

• Alternative hypothesis—a statement that the parameter falls in some alternative range

II. Identifies a correct test and checks appropriate conditions—this includes:

• Test statistic formula and substitution—identify the appropriate test and substitute values

• Check the assumptions or conditions needed to be able to use this test statistic—each test has certain conditions under which it applies.

III. Correct mechanics, including the value of the test statistic, df and P-value—this includes:

• Compute the test statistic—a description of how far the point estimate (our sample statistic) falls from the parameter value in the null hypothesis

• P-value—an objective measure of the strength of evidence which the data supplies in favor of the null hypothesis: the probability of getting a result as extreme or more extreme than the one observed if the proposed null hypothesis is correct.

IV. States a correct conclusion in the context of the problem, using the result of the statistical test—this includes:

• Select a significance level (alpha)—how certain we need to be of our decision related to confidence level: 95% confidence => 5% significance

• Conclusion (is p-value < alpha?)—a small p-value provides evidence against the null hypothesis, because data have been observed that would be unlikely if the null hypothesis were correct—reject the null hypothesis when the p-value is sufficiently small.

• Conclusion in the context of the question.

Hypothesis Test for a Proportion

1. Intro to your solution:

____________ the population characteristic to be tested ( p in words

state the _________________( [pic] ___

state the _________________([pic] ___

2. Check the conditions: ( if not met, state this and do the test anyway!

3. Identify the test you will use, show the substitution into the formula, sketch the bell curve, and have your calculator finish it:

4. Conclude in context: (is [pic]? if yes, reject [pic]; if no, fail to reject [pic]

state conclusion in the ______________ of the problem ( include level of significance

example: Your teacher claims to produce random numbers from 1 to 5 (inclusive) on her calculator, but you’ve been keeping track. In the past 80 selections, the number 5 has come up only eight times. You suspect that the calculator is producing fewer fives than it should. Run an appropriate significance test to test your claim.

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