Suppose that the underlying distribution function is symmetric, thus the mean is the same as the median, = m, representing the center. Suppose that we are interested in testing m(= ) = 75 against m > 75. We specify = .05, = .10 at m1 = 75.8 and variance 2 = 2.5 2 ( = 2.5).

(i) Suppose that the underlying distribution is N(, 2 ). Find the sample sizes for the tests based on the sample mean (z test) and the binomial test statistic (sample median). (ii) Suppose that the underlying distribution is double exponential with density

f

(

x

) =

2

e

|

x

|

.

Note that its variance ^2= 2/^2. Find the sample sizes for the tests based on the sample mean and the binomial test statistic (sample median).