Section 8.1 (p.441)

 

1.         (a) p(q) = Pr(Yn £ 1.5|q). If q £ 1.5, Pr(Yn £ 1.5) = 1. If q > 1.5, Pr(Yn £ 1.5) = (1.5/q)n. Therefore, the power function is

 

            (b) size a =supq³2 p(q) = supq³2 (1.5/q)n = (1.5/2)n = (3/4)2.

 

2.         (a) p(p) = Pr(Y ³ 7) + Pr(Y £ 1), which can be computed using the table of Binomial Probabilities. For example, p(0.2) = .0545+.0222+.0074+.0020+.0005+.0001+.0115+.0576 = .1558.

 

            (b) size a = p(0.2) = .1558.

 

3.        

where Z has the standard normal distribution. Therefore 5c = 1.96, c = 0.392.

 

4.         (a) simple

            (b) composite

            (c) composite

            (d) composite  (because the value of s is not specified)