a. A politician needs 50% or more of the vote to win an election. To find out how his campaign is going, he plans to obtain a random sample of 81 voters and see how many plan to vote for him. He is willing to posit a specific alternative hypothesis of 60% (or 40%) and wishes to use the .01 criterion of significance. Compute the power of the statistical test. How would you evaluate this research plan?

b. Suppose the politician decides to switch to the .05 criterion of significance (but that the other values are not changed). Will this improve the power of the statistical test to a satisfactory level?

c. The politician finally resigns himself to doing more work and obtaining a larger sample. He wants power to be .75. How large a sample does he need (using the .05 criterion)?