In April 2009, the Gallup organization surveyed 676 adults aged 18 and older and found
that 352 believed they would not have enough money to live comfortably in retirement. The folks at Gallup want to know if this represents sufficient evidence to conclude a majority (more
than 50%) of adults in the United States believe they will not have enough money in retirement.
(a) What does it mean to make a Type II error for this test?
(b) If the researcher decides to test this hypothesis at the a = 0.05 level of significance,
determine the probability of making a Type II error if the true population proportion is
0.53. What is the power of the test?
(c) Redo part (b) if the true proportion is 0.55.