A study of MBA graduates by University of Oregon Survey $1999$ revealed that MBA graduates have several expectations of prospective employers beyond their base pay. In particular, according tro the study $46\%$ expect a performance-based related bonus, $46\%$ expect stock options, $42\%$ expect a signing bonus, $28\%$ expect extra vacation, $25\%$ expect tuition reimbursement, $24\%$ expect health insurance and $19\%$ expect guaranteed annual bonuses. Suppose a study is conducted in an ensuing year to see whether these expectations have changed.
If $125$ MBa graduates are randomly selected and if $66$ expect stock options, does this result provide enough evidence to declare that a significantly higher proportion of MBAs expect stock options? Let $\alpha = 0.05$.
If the proportion really is $0.50$, what is the probability of committing a Type II error?
What is the probability of committing a Type II error if the figure is really $0.55$? $0.60$?
PS - I am thinking of using the Z distribution but I am not sure where to use the 46% who expect stock options. Help!