Question

What is the minimum sample size needed to estimate the mean age of the books in a library to within 2 months with 95% confidence if the standard deviation of the ages is thought to be about 60 months?

Answer #1

Solution :

Given that,

standard deviation = = 60

margin of error = E = 2

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_{/2}
= Z_{0.025} = 1.960

Sample size = n = ((Z_{/2}
*
) / E)^{2}

= (1.960 * 60) / 2)^{2}

=3457.44

= 3457

The minimum sample size = 3457

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