. (20 pts) An insurance company employs agents on a commission basis. It claims that in their rst year agents will earn a mean commission of at least $40,000 and that the population standard deviation is no more than $6,000. A random sample of nine agents found for commission in the rst year, 9 9 2x, =333 and Xxx-ff =312 i=1 '=l where x, is measured in thousands of dollars and the population distribution can be assumed to be normal. a. (10 pts) Test, at the 5% level, the null hypothesis that the population mean is at least $40,000. Clearly write you null and alternative hypothesis, compute your test statistics, state your decision rule and you conclusions. b. (10 pts) Test at the 10% level, the null hypothesis that the population standard deviation is at most $6,000. Clearly write you null and alternative hypothesis, compute your test statistics, state your decision rule and you conclusions