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Chapter 11

Chapter 11. More about Hypothesis Testing. Why Hypothesis Testing?. Before generalizing beyond the existing data, we must always measure the effect of chance; that is, we must obtain a value for the standard error. Incorrect decisions.

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Chapter 11

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  1. Chapter 11 More about Hypothesis Testing

  2. Why Hypothesis Testing? Before generalizing beyond the existing data, we must always measure the effect of chance; that is, we must obtain a value for the standard error.

  3. Incorrect decisions Even though we never really know whether a particular decision is correct or incorrect, it is reassuring that in the long run, most decisions will be correct – assuming the null hypotheses are either true or seriously false.

  4. Weak decision • Retain H0 = failure to reject H0 • The decision to retain H0 implies not that H0 is probably true, • but only that H0 could be true, • whereas the decision to reject H0 implies that H0 is probably false • (and the H1 is probably true).

  5. Supported by Strong Decision to Reject Because the research hypothesis is identified with the alternative hypothesis, the decision to reject the null hypothesis, should it be made, will provide strong support for the research hypothesis, while the decision to retain the null hypothesis, should it be made, will provide at most, weak support for the null hypothesis.

  6. Making the test more responsive • A two-tailed test is non-directional • Rejection region is located in both tails of the sampling distribution. • A one-tailed test is directional • Rejection region is located in just one tail of the sampling distribution.

  7. Decide before the hypothesis test! • If there is a concern that the true population mean differs from the hypothesized population mean only in a particular direction, use the appropriate one-tailed test for extra sensitivity. • Caution: you must retain H0 regardless of the how far the observed z deviates from the hypothesized population mean in the direction of “no concern.”

  8. Progress check 11.1 page 232

  9. Choosing a significance level

  10. Four possible outcomes

  11. True H0 usually retained • If H0 really is true, the probability of a type I error, α, equals the level of significance, and the probability of a correct decision equals 1 – α.

  12. Influence of sample size • To increase the probability of detecting a false H0, increase the sample size.

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