Refer to question 53. Suppose a random sample of the 12 partners reveals that 6 of them graduated from Ivy League schools and a random sample of 20 associates finds that 14 graduated from Ivy League schools:

(a) Find an estimate of the proportion of all lawyers in this firm who graduated from Ivy League schools.

(b) Construct a 99 % confidence interval for all lawyers in this firm who graduated from Ivy League schools.

Question 53

Suppose a large Wall Street law firm has 500 lawyers of whom 95 are partners and 405 are associates. A random sample of 15 partners finds that 11 own their own homes, and a random sample of 25 associates finds that 15 own their own homes.

(a) Find an estimate of the proportion of all lawyers in this firm who own their own homes, using an unbiased estimation procedure.

(b) Find a 95 % confidence interval for all lawyers in this firm who own their own homes.