Bacteria in bottled water. Is the bottled water you drink safe? According to U.S

Question

Bacteria in bottled water. Is the bottled water you drink safe? According to U.S. News & World Report, the Natural at Resources Defense Council warns that the bottled water you are drinking may contain more bacteria and other potentially carcinogenic chemicals than allowed by state and federal regulations. Of the more than I,000 bottles studied, nearly one-third exceeded government levels. Suppose that the Natural Resources Defense Council 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 plusminus 0.01 with 99% confidence.

Explanation / Answer

as here p =1/3

also margin of error E =0.01

and for 99% CI, z =2.5758

therefore from the formula n=p(1-p)(Z/E)2

required sample size n =(1/3)(1-1/3)(2.5758/0.01)2 =14745 as we have to round it up to get minimum value of sample size.

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