This is personal study note Copyright and original reference: https://www.youtube.com/watch?v=pd6is0rKISA&list=PLsri7w6p16vulKaxOlNQFSWuyDuE9oEVP ================================================================================ Decide number of sample ================================================================================ Large sample data: good, credibility increases $$$\bar{X} \pm z_{\frac{\alpha}{2}} \times \text{standard error} \\ $$$ $$$= \bar{X} \pm z_{\frac{\alpha}{2}} \times \frac{\sigma}{\sqrt{n}}$$$ ================================================================================ Simplify above equation with respect to n ================================================================================ c n: proper size of sample from the population $$$ n = \dfrac{z_{\frac{\alpha}{2} \times \sigma}}{d} $$$ $$$ n = \left \dfrac{z_{\frac{\alpha}{2} \times \sigma}}{d} \right^2 $$$ d: allowed error ================================================================================ confidence: 99% z=2.58 allowed error += 100ml d=100 population_std: 150ml population_std=150 ================================================================================ confidence: 99% z_half_alpha=2.58 d=100 When you don't know population std, you extract 10 number of samples to calculate sample_std sample_std=170