Question

Find the minimum sample size n needed to estimate mu for the given values of​ c, sigma​, and E. cequals0.95​, sigmaequals7.7​, and Eequals2 Assume that a preliminary sample has at least 30 members.

Answer 1

Solution

standard deviation = =7.7

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 = Z0.025 = 1.96 ( Using z table ( see the 0.025 value in standard normal (z) table corresponding z value is 1.96 )

sample size = n = [Z/2* / E] 2

n = ( 1.96* 7.7 /2 )2

n =56.9

Sample size = n =57