Chapter 18 Practice Quiz × Home | 18.5 The two error (top curve, -0) and of a Ty

Question

Chapter 18 Practice Quiz × Home | 18.5 The two error (top curve, -0) and of a Type curves in Figure 18.1 are used to find the probabilities of a Type I error (bottom curve, -08) . Lounhod Online Resources . The StatBoards video, Power, Type 1, and Type II Errors, provides examples of calculating power, type I, and type ll errors Apply Your Knowledge 18.14 What Is Power? The Trial Urban District Assessment (TUDA) measures progress within participating large urban districts TUDA gives a reading test scored fom 0 to 500 A score of 243 is a "basic" reading level for 5 Suppose scores on the TUDA reading test for eighth-graders in your district follow a Normal distribution with standard devation -55. In 2013 the mean score for eighth graders in your district was 255. You plan to give the reading test to a randon sample of 25 eighth- graders in your district thas year to test whether the mean score for all eighth-graders in your district is still above the basic level. You will therefore test Hr > 243 If the true mean score is again 255, on average students are performing above the basic level You learn that the power of your test at the 5% significance level against the alternative -255 is 0.29. (b) Explain why the test you plan will not adequately protect you against deciding that average reading scores in your district are not abote basic level

Explanation / Answer

(a)

The power of a test is the probability that we make the right decision when the null is not correct (i.e. we correctly reject it). So, power = 0.29 means that the probability that we make the right decision when mean score is greater than 243 is 0.29. That is when the mean score is actually greater than 243, there is 29% chance that we correctly identify this in the test.

(b)

When the mean score is actually greater than 243, there is 71% (100 - 29 %) chance that we incorrectly identify this in the test and predict that the mean score is not above basic level. As this percentage is high, the test would not adequately protect against deciding that average reading scores in the district are not above basic level.

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