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 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 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 plus-minus sign 0.01 with 99% confidence.

Explanation / Answer

for the sample size n:

n = N*X / (X + N – 1),

where,

X = Z/22 ­*p*(1-p) / MOE2,

and Z/2 is the critical value of the Normal distribution at /2 = 2.576 (from Z table)

MOE is the margin of error = +/- 0.01

p is the sample proportion = 333

and N is the population size = 1000

Substituting the above values, we get

X = 14450

N = 936

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