Question

If you want to be 99?% confident of estimating the population mean to within a sampling error of plus or minus 35 and the standard deviation is assumed to be 140?, what sample size is? required?

Answer 1

Solution :

Given that,

standard deviation = = 140

margin of error = E = 35

At 99% confidence level the z is ,

  = 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z_/2 = Z_0.005 = 2.576

Sample size = n = ((Z_/2 * ) / E)²

= ((2.576 * 140) / 35)²

= 106.17 = 107

Sample size = 107