Question: A study based on a sample of 64 males from the United States over the age of 50, found that 32 men suffered from an enlarged prostate.

1. In words, state the population parameter of interest.
2. The 95% confidence interval formula for the population proportion is based on the central limit theorem. State the conditions/assumptions to use this formula
3. Calculate a 95% confidence interval for the population parameter
4. What is the margin of error for the 95% confidence interval?
5. If we calculated a 99% confidence interval, as compared to your answer in part b, would your margin of error increase: (choose one)
   1. increase
   2. decrease
   3. stay the same
6. If we increase the sample size to 100 persons, but the reported sample mean and sample standard deviation stayed the same as in part a, would the 95% confidence interval get: (choose one)
   1. wider
   2. narrower
   3. stay the same
7. Assuming that 50% of men over the age of 50 have an enlarged prostate in the US. What sample size would you have to use to achieve a margin of error for a 95% confidence interval to be half as large as the current margin of error based on 64 people?