Bacteria in bottled water. Is the bottled water you drink safe? The Natural Resources Defense Council warns that the bottled water you are drinking may contain more bacteria and other potentially carcinogenic chemicals than are allowed by state and federal regulations.
Of the more than 1,000 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 {0.01 with 99% confidence.
Answer: We have the level of significance alpha = 0.01. From the above figure shows that the area in each of the red-shaded tails is alpha/ 2 = 0.005. We find z alpha/2 = 2.5758 by noting that the cumulative area to its left must be 1 0.005 or 0.995. We can use the standard normal table values to find the area of 0
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