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Chapter 9

Chapter 9. Testing a Claim. Significance Test. A significance test is a formal procedure for comparing observed data with a claim (also called a hypothesis ) whose truth we want to assess. The claim is a statement about a parameter: Population proportion p Population mean

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Chapter 9

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  1. Chapter 9 Testing a Claim

  2. Significance Test • A significance test is a formal procedure for comparing observed data with a claim (also called a hypothesis) whose truth we want to assess. • The claim is a statement about a parameter: • Population proportion p • Population mean • We express the results of a significance test in terms of probability that measures how well the data and the claim agree.

  3. Stating Hypotheses • Null Hypothesis (– This is the claim tested by a statistical test. Often this is a statement of “no difference.” • Alternative Hypothesis () – This is the claim about the population that we are trying to find evidence for.

  4. For Example… • Mr. Suk thinks he is an 80% free throw shooter: • The national mean AP score is 2.51. A study of 20 randomly selected AP students from LNHS found the mean score on the AP Exam.

  5. One-sided vs. Two-sided • The alternative hypothesis is one-sided if it states that a parameter is larger or smaller than the null hypothesis. • It is two-sided if it states that the parameter is different from the null hypothesis (it could be larger or smaller).

  6. P-Value • The probability that the statistic (such as or ) would take a value as extreme as or more extreme that the one actually observed is called the P-value of the test. • The smaller the p-value, the stronger the evidence against • We compute these assuming is true • Note: the null is at the peak of this curve!

  7. Example • Mike is testing new golf clubs to see if they perform better than his old clubs. His average drive with the old clubs was 243 yards. When Mike was testing his new golf clubs, a significance test using the sample data produced a p-value of 0.002. • Interpret the P-value in context: • Do the data provide convincing evidence against the null hypothesis? Explain.

  8. In a nutshell… • Our conclusions in a significance test comes down to: • P-value smallin context • P-value large in context • WHY?!?! (think about Mr. Suk with basketball)

  9. Statistically Significant • What is a small enough p-value to reject? • 20%? • 15%? • …? • If the p-value is smaller than alpha, we say that the data are statistically significant at level . In that case, we reject and conclude that there is convincing evidence in favor of

  10. Example: Battery Problem • A company has developed a new deluxe AAA battery that is supposed to last longer than its regular AAA battery, but these are more expensive to produce so the company would like to be convinced that they really do last longer. They know that the regular AAA battery last for 30 hours, on average. The company selects a SRS of 15 new batteries and uses them until they are completely drained. What are the hypotheses in question?

  11. Battery Problem Continued: • The resulting p-value is 0.0276. What conclusions can you make for the following significance levels?

  12. Homework* • Pg. 546 (1-17)*

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