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Imagine that a sample of 400 rental units shows that (i) the distribution of rents paid per month is not described by a normal distribution,
(ii) that the mean rent of the sample is $755, and (iii) the standard deviation of the sample is $100.
a) Without seeing the distribution, can you calculate the probability that the rent of a randomly selected unit will be greater than $800? If yes, calculate the probability; if no, explain.
b) Without seeing the distribution, can you calculate the probability that the mean rent of another sample of 400 units will be greater than $800? If yes, calculate the probability; if no, explain.
c) Why is the answer to (b) only an estimate? (What two numbers about the entire population are you not sure of?)
What is a hypothesis test? Why do we need to use them to make decisions about relating sample results to the population; why can’t we just make our decisions by the sample value?
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