Question

How do you find the sample size with only knowing the Standard Deviation, Confidence interval, and sample mean?

Also if there is no sample mean given?

Answer 1

Sample size formula is given by

where , n is the sample size

is the standard deviation

E is the margin of error , which is the half of length of confidence interval

that is , E= ( upper limit - lower limit) / 2

is the critical value which is based on the confidence level

that is for 95% confidence level , = 1.96

for 99% confidence level ,   = 2.56

etc

For example

suppose 95% confidence interval is (28.44, 38.96)

Also =12

E = (38.96-28.44)/ 2= 5.26

For 95% confidence , =1.96

Thus we get, n = ( 1.96*12/ 5.26)² = 20

Note : Sample mean is not necessary  to calculate the sample size