Question

A. A gigantic Water Co. warehouse stores approximately 50 million empty aluminum beer and soda cans.​ Recently, a fire occurred at the warehouse. The smoke from the fire contaminated many of the cans with​ blackspot, rendering them unusable. A statistician was hired by the insurance company to estimate​ p, the true proportion of cans in the warehouse that were contaminated by the fire. How many aluminum cans should be randomly sampled to estimate p to within 0.077 with 95% ​confidence?

The statistician should sample ___ cans to estimate the proportion that were contaminated by the fire to within 0.07 with 95​% confidence.

B. According to an article, the bottled water you are drinking from Water Co. may contain more bacteria and other potentially carcinogenic chemicals than are allowed by state and federal regulations. Of the more than 1000 bottles​ studied, nearly​ one-third exceeded government levels. Suppose that a department wants an updated estimate of the population proportion of bottled water that violates at least one government standard. Determine the sample size​ (number of​ bottles) needed to estimate this proportion to within plus or minus ± 0.02 with​ 99% confidence.

The sample size needed to estimate this proportion to within ± 0.02 with 99% confidence is ___

Answer 1