*6A.6. *Suppose *n *= 36 observa tions are taken from a normal distribution where *a *= 8.0 for the purpase of testing Ho:µ = 60 versus *H**1 **: **µ ****60 at the *tt *= 0.07 level of significance.

The lead investigator skipped statistics class the day decision rules were being dis.cussed and intends to reject Ho if *y *falls i n the region (60 - *y• **, *60 + *y• **).*

(a) Find *y" .*

(b) What is the power of the test when µ = 62?

(c:) What would the power of the test be when *µ *= 62 if the critical region had been

defined the correct way?

ti.4.7. If Ho:µ, = 200 is to be tested against H1:*µ, * 200 at the *a** *= 0.10 level of significance based on a random sample of size *n** *from a normal distribution where *CT** *= 15.0. what is the smaUest value for *n** *th at will make the power ei!Ual to at least 0.75 when µ, = 197?

6.4..8. Will *n *= 45 be a sufficiently large sample to test *Ho: µ, *= 10 versur; H1.*µ** **=I' *10 at the

*a *= 0.05 level of significa nce if the experimenter wants the Type II error probability to be no greater than 0.20 when *f--L *= 12? Assume that *CT *= 4.

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