Your company is carrying out tests on a new pharmaceutical product which has the potential to treat a serious disease. From a sample of 250 persons in the trial, 162 report improvement in their symptoms over a three-month period. You wish to carry out a test to see if the population proportion improvement rate is better than the rate for the drug currently in use, which improves the symptoms of 60% of patients.

1. State the null and alternative hypotheses in statistical terms.
2. Explain the risks associated with Type I and Type II errors in this context.
3. Which type of error do you consider to be more serious?