Answer to Question #94396 in Statistics and Probability for amita

Question

3) Mr. Alok is a purchasing agent of electronic calculators. He is interested in determining at a confidence level of 95% what proportion (within plus or minus 4%), is defective. Conservatively, how many calculators should be tested to find the proportion defective?

Answer 1

We have been given the following:

Population is infinite;

e = 0.04 (since the estimate should be within 4% of the true value);

z = 1.96 (as per table of area under normal curve for the given confidence level of 95%)

As we want the most conservative sample size we shall take the value of p = 0.5 and q =0 .5.

We can determine the sample size :

$$n={z^2pq \over e^2}$$ $$n={1.96^2(0.5)(0.5) \over 0.04^2}=600.25\approx600$$

Thus, the most conservative sample size needed for the problem is 600.