8.6-14 (slightly modified): Consider the distributions

N(\\\\mu _(x),400)

and

N(\\\\mu _(Y),225)

. Let\

\\\\theta =\\\\mu _(x)-\\\\mu _(Y)

. Say

\\\\bar{x}

and

/bar (y)

denote the observed means of two independent random samples,\ each of size

n

, from the respective distributions. Say we reject

H_(0):\\\\theta =0

in favor of

H_(1):\\\\theta >0

\ if

\\\\bar{x} (-)/(b)ar (y)>=c

. Let

K(\\\\theta )

be the power function of the test. Find

n

and

c

so that

K(0)=0.05

and\

K(10)>=0.90

. In other words, find

n

and

c

so that the test has significance level

\\\\alpha =0.05

, with\ power at least 0.9 when the true mean difference

\\\\theta =10

.

8.6-14 (slightly modified): Consider the distributions N(X,400) and N(Y,225). Let =XY. Say x and y denote the observed means of two independent random samples, each of size n, from the respective distributions. Say we reject H0:=0 in favor of H1:>0 if xyc. Let K() be the power function of the test. Find n and c so that K(0)=0.05 and K(10)0.90. In other words, find n and c so that the test has significance level =0.05, with power at least 0.9 when the true mean difference =10