5. (20%) Let X be a random variable with mean /.i and finite varianceσ
2. Wc want to test the hypotheses
,
where /iq is specified. Let X1, • • •, X
n be a random sample from the distribution of X and denote the sample mean and variance by
and S
2respectively.
【題組】
(a) Find the decision rule with the approximate size a of the test.