Sickle-cell disease is a potentially lethal genetic disease in the Black race. It is estimated that 30% of African-Americans in a certain Gulf Coast region have the disease or carry the trait for it. This figure seems too large to a physician in the region, so he takes a random sample of 25 of his African-American patients and examines blood smears.
a. State the physician's most logical null and alternative hypotheses.
b. What region of rejection would you suggest he use? What is the a level for this region?
c. If the percentage in question is really 15%, what is the power of his test?
d. Which type of error is more serious in his study, Type I or Type II? Why?
e. Suppose 12 patients of his sample have the condition or seem to be genetic carriers. Should he reject his null hypothesis or not? Why? What is the P value? What conclusion should he draw about the proportion of sickle-cell disease in the Black population?