The city council in a large city has become concerned about the trend toward exclusion of renters with children in apartments within the city. The housing coordinator has decided to select a random sample of 125 apartments and determine for each whether children are permitted. Let p be the proportion of all apartments that prohibit children. If the city council is convinced that p is greater than 0.75, it will consider appropriate legislation.
a. If 102 of the 125 sampled apartments exclude renters with children, would a level .05 test lead you to the conclusion that more than 75% of all apartments exclude children?
b. What is the power of the test when p = .8 and α = .05?