In each of the following situations, data are obtained by conducting a statistical study. Classify each statistical study as experimental or correlational. Statistics students collect data on the shower length and gender of the person taking the shower for a random sample of showers. The manager of a tuna canning factory is interested in finding out which set of machine settings results in a smaller variance of the fill weight of the tuna cans. She uses one set of machine settings for the day shift and a second set of settings for the night shift. The next day she uses the second set of settings for the day shift and the first set of settings for the night shift. Data are collected on the fill weights of the tuna cans. For a sample of college students using the ATM in the campus center, data are collected on the dollar amount withdrawn.

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.