A large company would like to estimate the true proportion of defects from a very large lot of electronics parts from a vendor. The vendor claims the true proportion is p = 0.05. To conduct such a study, there is an overall set-up cost of $500 and the $2 for each part tested (which is destroyed during testing). The statistician's total budget for this study is $4100. Assume that each part sampled and tested is Bernoulli (p) and that the sample represents fixed Bernoulli trials.
(a) With 95% confidence, what is the smallest error of estimate one can achieve within this budget?
(b) If a sample of the size computed above is drawn from the lot and the sample proportion was phat = 0.06, calculate and interpret a 95% confidence interval on the true proportion defectives.
(c) Do the data support or provide evidence against the vendor's claim? Explain.