Assume that we have an iid sample {Xi}n

i=1 with mean and standard devi

ation and they are continuous random variables. Circle the correct answer.

(a) (2 pts) Although n is very large (say, n=1000), we can not expect for the sample

mean to be exactly equal to .

TRUE FALSE

(b) (2 pts) The t-confifidence interval for is valid even though we do not have nor

mality assumption for Xi 's.

TRUE FALSE

(c) (2 pts) Given the test statistic, we can fifind the appropriate sample size n to keep

both Type I and Type II error probability low at some desired levels.

TRUE FALSE

(d) (2 pts) To calculate , we need 0 (or a), the alternative value for , which need

to be assumed as the true parameter.

TRUE FALSE

(e) (2 pts) In HT, failing to reject H0 means that we have empirical evidence to

support H0 (especially for small ).

TRUE FALSE