How large a sample is needed so that a 95 confidence interva

How large a sample is needed so that a 95% confidence interval for the mean number of years of attained education has a margin of error equal to one year? you could assume the range that the values of number of years of educational attainment fall within (e.g., from 0 to 18 years) and the distribution is approximately normal.

Solution

How large a sample is needed so that a 95% confidence interval for the mean number of years of attained education has a margin of error equal to one year? you could assume the range that the values of number of years of educational attainment fall within (e.g., from 0 to 18 years) and the distribution is approximately normal.

Z value at 95% =1.96

margin of error =d=1

sd =range /4 =18/4=4.5

n=z²*s²/d² = 1.96² * 4.5²/1² =77.7924

The required sample size =78