Question

Determine the minimum sample size required when you want to be 95​% confident that the sample mean is within one unit of the population mean and sigmaequals13.7. Assume the population is normally distributed. A 95 % confidence level requires a sample size of nothing. ​(Round up to the nearest whole number as​ needed.)

Answer 1

Solution :

Given that,

standard deviation = = 13.7

margin of error = E = 1

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 * 13.7) / 1)²

= 721.03

= 721

Sample size = 721