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Solution: D

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Chapter 20Testing Hypotheses About Proportions

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Steps to Hypotheses Testing:Step One: Write your hypotheses: Our starting hypothesis is called the null hypothesis,

denoted H0. The alternative hypothesis is denote by HA. There are three possible alternative hypotheses:

HA: parameter < hypothesized value (one-sided) HA: parameter ≠ hypothesized value (two-sided) HA: parameter > hypothesized value (one-sided)

Example: A large city’s Department of Motor Vehicles claimed that 80% of candidates pass driving tests, but a newspaper reporter’s survey of 90 randomly selected local teens who had taken the test found only 61 who passed. Does this finding suggest that the passing rate for teenagers is lower than the DMV reported? Write appropriate hypotheses.

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Step two: Model Check assumptions and conditions and specify the model

you will use to test the null hypothesis. Independence Assumption Randomization Condition 10% Condition Success/Failure Condition Your model step should end with a statement such

Because the conditions are satisfied, I can model the sampling distribution of the proportion with a Normal model. Then state the parameters of the Normal model.

If the assumptions and conditions are not met you may need to write “Because the conditions are not satisfied, I can’t proceed with the test.” If that’s the case, stop and reconsider.

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For now, our only test (the test about proportions) is the one-proportion z-test. You will need to find:

p-hat

SD =

z

Example: A large city’s DMV claimed that 80% of candidates pass driving tests. A reporter has results from a survey of 90 randomly selected local teams who had taken the test. Are the conditions for inference satisfied?

n

pq

n

pq

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Step Three: Mechanics

Find the P-Value.

Example: What is the P-value for the one-proportion z-test?

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Step Four: Conclusion The conclusion in a hypothesis test is always a

statement about the null hypothesis. The conclusion must state either that we reject or that we fail the reject the null hypothesis.

Example: What can the reporter conclude? And how might the reporter explain what the P-value means for the newspaper story?

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P-Values and Decisions:What to Tell About a Hypothesis Test

How small should the P-value be in order for you to reject the null hypothesis?

It turns out that our decision criterion is context-dependent. When we’re screening for a disease and want

to be sure we treat all those who are sick, we may be willing to reject the null hypothesis of no disease with a fairly large P-value (0.10).

A longstanding hypothesis, believed by many to be true, needs stronger evidence (and a correspondingly small P-value) to reject it.

Another factor in choosing a P-value is the importance of the issue being tested.

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P-Values and Decisions (cont.)

Your conclusion about any null hypothesis should be accompanied by the P-value of the test. If possible, it should also include a confidence

interval for the parameter of interest. Don’t just declare the null hypothesis rejected or

not rejected. Report the P-value to show the strength of the

evidence against the hypothesis. This will let each reader decide whether or not

to reject the null hypothesis.

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Example: (#32) The College Board reported that 60% of all students who took the 2006 AP Stats exam earned scores of 3 or higher. One teacher wondered if the performance of her school was different. She believed that year’s students to be typical of those who will take AP Stats at that school and was pleased when 65% of her 54 students achieved scores of 3 or better. Can she claim that her school is different? Explain.

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What Can Go Wrong?

Hypothesis tests are so widely used—and so widely misused—that the issues involved are addressed in their own chapter (Chapter 21).

Don’t accept the null hypothesis.

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What have we learned?

We’ve learned: Start with a null hypothesis. Alternative hypothesis can be one- or two-sided. Check assumptions and conditions. Data are out of line with H0, small P-value, reject

the null hypothesis. Data are consistent with H0, large P-value, don’t

reject the null hypothesis. State the conclusion in the context of the original

question.

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Homework: Pg. 476 1, 11-21 odd