Suppose you wish to estimate the difference between the mean acidity for rainfal

Question

Suppose you wish to estimate the difference between the mean acidity for rainfalls at two different locations, one in a relatively unpolluted area and the other in an area subject to heavy air pollution. If you wish your estimate to be correct to the nearest 0.2 pH, with probability near 0.90, approximately how many rainfalls (pH values) would have to be included in each sample? (Assume that the variance of the pH measurements is approximately 0.4 at both locations and that the samples will be of equal size. Round your answer up to the nearest whole number.)

Explanation / Answer

Answer to the question is as follows:

So, We have the margin of error as

MOE = Z*sqrt( p *p'/n)

.2 = sqrt(.9*.91/n)

So, n >= .9*.91/.2^2 = 20.475 or 21

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