7.102 Apartment rental rates. You hope to rent an unfurnished one-bedroom apartment in Dallas next year. You call a friend who lives there and ask him to give you an estimate of the mean monthly rate. Having taken a statistics course recently, the friend asks about the desired margin of error and confidence level for this estimate. He also tells you that the standard deviation of monthly rents for one-bedrooms is about $300.
(a) For 95% confidence and a margin of error of $150, how many apartments should the friend randomly sample from the local newspaper?
475
(b) Suppose that you want the margin of error to be no more than $50. How many apartments should the friend sample?
(c) Why is the sample size in part (b) not just nine times larger than the sample size in part (a)?