You are at a magic show. The magician has a coin and you, as a member of the audience, do not know whether the coin has heads on both sides or heads on one side and tails on the other. The null hypothesis is that the coin has heads on one side and tails on the other (with both heads and tails being equally likely), and the alternative hypothesis is that the coin has heads on both sides (so that the coin will always land heads). The magician tosses the coin five times, and you use the test statisticX = number of heads in the five tossesYou decide that you will reject the null if all five tosses end up being heads, and otherwise you will accept the null hypothesis. Answer the following questions. Hint: you do NOT need Z statistics or T statistics to answer the questions below! You just need to think and use basic probability.
(a) Identify Type I and Type II errors for this test procedure.
(b) Calculate the probability of a Type I error.
(c) For what values of X will you accept the null hypothesis?
(d) Calculate the probability of Type II error for this test.
(e) Calculate the power of this test.