7 A drug for treating a particular minor illness cures, on average, \(78 \%\) of patients. Twenty people with this minor illness are selected at random and treated with the drug.
- \(( A )\) Find the probability that exactly 19 patients are cured.
(B) Find the probability that at most 18 patients are cured.
\(( C )\) Find the expected number of patients who are cured. - A pharmaceutical company is trialling a new drug to treat this illness. Researchers at the company hope that a higher percentage of patients will be cured when given this new drug. Twenty patients are selected at random, and given the new drug. Of these, 19 are cured. Carry out a hypothesis test at the \(1 \%\) significance level to investigate whether there is any evidence to suggest that the new drug is more effective than the old one.
- If the researchers had chosen to carry out the hypothesis test at the \(5 \%\) significance level, what would the result have been? Justify your answer.