As bridge building, craftily clever Calpurnia does dazzlingly double-duty dinners, emcee-ing elegant, elegiac, eleemosynary events: for forty-four favorite uffy fat-cats, Georgia'sgolden girl gladly helps heavy hitters initiate inimitable joviality. In Calpurnia's experi-ence the population of all her donations is approximatelyNormally distributed. TonightCalpurnia's 44 fat-cats donate $27,500, with Standard Deviations s= $125. Required:
a. Estimate the mean donation for Calpurnia's population of fat-cats.
b. To draw any inferences from these data, what must we assume about the population of fat-cat donations, and why? We shall assume this for the remainder of this problem.
c. For Calpurnia's sample of 45 donors, suppose that s = $120.

i. Find a 90% confidence interval for Calpurnia's population mean donation.
ii. Find a 98% confidence interval for Calpurnia's population mean donation.
iii. Compare your answers in c. i. and c. ii.: which interval is wider, and why?

d. Calpurnia believes she can rake in more than $400 per party-goer, on average. What hypotheses should she use to test this? Define in words any parameters.
e. To test these hypotheses, what test-statistic should Calpurnia use?