(Need help, I’m taking a test) A television newscaster from a 24-hour news station wants to estimate the number of hours per day its viewers watch programming on this channel. The newscaster randomly selects 100 viewers and asks them
how many hours per day they watch this station. The newscaster constructs an 85% confidence interval for
the true mean number of hours viewers watch this station. Which of the following would decrease the margin
of error?
using a sample of size 50
using a sample of size 200
constructing a 90% confidence interval
constructing a 95% confidence interval

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.