63. The error X in a measurement has a normal distribution with mean value 0 and variance s2. Consider testing H0: s2  2 versus Ha: s2  3 based on a random sample X1, . . . , Xn of errors.

gxi  c pˆ  x/n  .21 X x  74

a. Show that a most powerful test rejects H0 when

.

b. For n  10, nd the value of c for the test in (a)

that results in a  .05.

c. Is the test described in

(a) UMP for H0: s2  2 versus Ha: s2 2? Justify your assertion.