The sample size needed to estimate the difference between two population proport

Question

The sample size needed to estimate the difference between two population proportions to within a margin of error E with a significance level of alpha can be found as follows in the expression E = z* squareroot p_1 (1 - p1)/n_1 + p_2 (1 - p_2)/n_2 we replace both n_1 and n_2 by n (assuming that both samples have the same size) and replace each of p_1, and p_2, by 0.5 (because their values are not known) Then we solve for n and get. N = (z*)^2/2e^2. Finally, increase the value of n to the next larger integer number. Use the above formula and Table C to find the size of each sample needed to estimate the difference between the proportions of boys and girls under 10 years old who are afraid of spiders. Assume that we want a 96% confidence level and that the error is smaller than 0.09.

Explanation / Answer

n = (z)^2 / (2E^2)

We are given,

E = 0.09

zc we need to find from normal table as 2.054

n = (2.054)^2/(2*0.09)^2

   = 260.43

The nearest number is 260.

Answer: 260

Note: If we take the next digit then the answer is 261.

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