6.4.1. Recall the "Math for the Twenty-First Omtury" hypothesis test done in Example 6.2.1. Calculate the power of that test when the true mean is 500.

6..4.2. Carry out the details to verify the decision rule change cited on page *451 *in connection

with Figure 6.4.6.

6.4..3. For the decision rule found in Question 6.2.2 to test *Ho:** **µ** *= 95 versus H1:*µ.** *.,;,. *95** *at the

*a *= 0.06 level of significance, calculate J - *f3 *when *µ, *= 90.

6.4.4. Construct a power curve for the *a *= *0.05** *test of *Ho: **µ. *= 60 versus Hi: *µ *** *60 if the data

consist of a random sample of size 16 from a normal distribution having *a *= 4.

6.4.S. If *Ho: µ *= 240 is tested against H1: *µ * 240 at the *a *= 0.01 level of significance with a random sample of 25 normally dist ributed observations, what proportion of the time will the procedure fail to recognize that *µ *has dropped to 220? Assume that *a *= 50.

* *

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