Question

To be able to say with 99% confidence level that the stadard deviation of a data set is 10% within the population's standard deviation, the number of observations within the data set mist be within what quantity? I know the answer is n=336 and my teacher mentioned its from a table but didn't include it. How can I solve this? And what table is this value from?

Answer 1

The sample size formula to estimate population standard deviation within d is:

n = 1/2(z_α/2 /d )²

We are given d = 10% = 0.1

for 99% confidence level, critical value of z is z_α/2 =2.58

Small Table of z-values for Confidence Intervals

Confidence Level	z
0.70	1.04
0.75	1.15
0.80	1.28
0.85	1.44
0.90	1.645
0.92	1.75
0.95	1.96
0.96	2.05
0.98	2.33
0.99	2.58

Therefore, the required sample size is:

n = 1/2 (2.58/0.1)² = 665.64/2 = 332.82 ~ 333

**Please ask if you have any doubt, happy to help you.Thank you.