Assume that is a random sample from
, with
. We want to test
against
. For a fixed integer
, the following statistics are defined:
Fix .
Consider the test
Reject if
Find a choice of in terms of the standard normal distribution function
that ensures that the size of the test is at most
.
Show that the problem is equivalent to finding that
Use Boole's Inequality o get
Show that under ,
~
. Hence, find
See the full solution below.