Assignment task: An engineer is constructing a confidence interval to estimate the population proportion p of cracked glass panels supplied by company X. To better inform his boss, any such interval is allowed a total width of 10% only (e.g., "percentage of cracked panels is estimated to be between 22% to 32%"), regardless of the sample size or confidence level used.
(a) If there is a prior rough estimate of p available at 0.32 while a 99% confidence level is needed, what is the minimum required sample size?
(b) Without any prior information on p, while a confidence level of 98% is needed, what is the minimum required sample size?
(c) If the sample size is limited to 100 due to budgetary concerns, while the p ~ 0.32 prior estimate is valid. What level of confidence will the estimation interval have?