To study what fraction of houses for sale in Victoria has a finished basement, a researcher selected a random sample of 20 houses that were on the market. It was found that 11 of the houses surveyed did in fact have a finished basement.

(a) Using the random sample collected by the researcher, calculate a 95% confidence interval for the proportion of houses for sale in Victoria that have a finished basement.

(b) After calculating a confidence interval for the proportion of houses for sale in

Victoria that have a finished basement, the researcher felt that the obtained confidence interval was probably too wide to be of any practical use to realtors or potential buyers. So the researcher would like to collect a larger sample of houses for sale in order to get a better estimate. The desired confidence interval is still a 95% confidence interval, and the researcher can make use of the estimate for p from the initial sample in order to decide on what sample size to use. What sample size should now be collected in order to estimate the true proportion of houses for sale in Victoria that have a finished basement to within 0.05?