Question

As bridge building, craftily clever Calpurnia does double duty dinners, emceeing elegant, elegiac, eleemosynary events; for forty favorite fat-cat friends, Georgia’s golden girl gladly helps heavy hitters initiate inimitable joviality. At her current bash, Calpurnia entertains 25 revelers who shell out $12,500 to donate to charity.

Suppose Calpurnia believes that the standard deviation of her entire population of fat-cat fleecings is more like σ = $100.

i. What must we assume about our sampling population, and why?

ii. Find a 96% confidence interval for Calpurnia’s mean donation.

iii. Find and compare a 99% confidence interval for her mean donation.

iv. What hypotheses should she use to test this? Define any parameters.

Answer 1

Clearly 99% confidence Interval is more wider than 95% confidence interval.

iv. Here the population parameter of interest is the population mean

And she should use two tailed test for mean to test the mean value and should use Z statistic because the population standard deviation is known.