Bacteria in Bottled Water: Is the bottled water you drink safe? According to an
ID: 3174760 • Letter: B
Question
Bacteria in Bottled Water: Is the bottled water you drink safe? According to an article in U.S. News and World Report (April 12, 1999) the Natural 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 1000 bottles studied previously nearly 1/3 exceeded government levels. Suppose that the Natural Resources Defense Council wants an updated estimate of the population proportion of bottle water that violates at least one government standard. Determine the minimum number of bottles needed to estimate the true proportion to within 0.01 with a 99% confidence level. If there was no prior estimates available, how many bottles should be tested?Explanation / Answer
a. Required number of bottles needed to be estimated, n=phatg(1-phatg){(z alpha/2)/E}^2, where, phatg denotes proportion of educated guess, n is sample size, and z denotes z critiical at alpha/2, and E is margin of error.
={1/3(1-1/3)}(2.576/0.01)^2
=29492.3~29492 (ans)
b. If there is no prior estimates available, assume phatg=0.5.
n=0.25(2.576/0.01)^2
=16589.44~16589
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