Select the appropriate test for each of the following situations.
(1) An economist wants to know if there is an association between a movie's planned budget and the total revenue made opening weekend.
(2) A wildlife biologist wants to see if the average nesting time for peregrine falcons who live more than 3 miles from a body of water is greater than the known nesting time of 4.3 weeks for falcons who live within 3 miles of a body of water.

a) One Proportion Z Test
b) One Sample T-Test
c) Two Proportion Z Test
d) Independent Samples T-Test
e) Paired T-Test
f) Simple Linear Regression

Aprisoner is trapped in a cell containing three doors. the first door leads to a tunnel that returns him to his cell after two days of travel. the second leads to a tunnel that returns him to his cell after three days of travel. the third door leads immediately to freedom. (a) assuming that the prisoner will always select doors 1, 2 and 3 with probabili- ties 0.5,0.3,0.2 (respectively), what is the expected number of days until he reaches freedom? (b) assuming that the prisoner is always equally likely to choose among those doors that he has not used, what is the expected number of days until he reaches freedom? (in this version, if the prisoner initially tries door 1, for example, then when he returns to the cell, he will now select only from doors 2 and 3.) (c) for parts (a) and (b), find the variance of the number of days until the prisoner reaches freedom. hint for part (b): define ni to be the number of additional days the prisoner spends after initially choosing door i and returning to his cell.