Question

determine the minimum sample size required when you want to be 95% confident that the sample mean is within 1.4 unites of the population mean. Assume that the population is normally distributed with standard deviation σ = 4.7

1. whats the critical value?

2. whats the margin of error?

3. whats the sample size?

Answer 1

Solution

standard deviation =   =4.7

Margin of error = E = 1.4

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 = 1.96 ( 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*4.7 / 1.4 )²

n =43.29

Sample size = n =43