In each of the following, determine whether the conditions for conducting a z -test for a proportion are met. If not, explain why not.

(a) (3 point) A company employs 500 stockbrokers. They are all surveyed to find out whether a majority believes the market will go up in the next year. H0 : p = 0.50; Ha : p > 0.50.

(b) (3 point) A market research firm wants to know whether more than 30% of the people who visit a mall actually buy something. A researcher stands by the exit door starting at noon and asks 50 people as they are leaving whether they bought anything. H0 : p = 0.30; Ha : p > 0.30.