This is personal study note
Copyright and original reference:
https://www.youtube.com/watch?v=pd6is0rKISA&list=PLsri7w6p16vulKaxOlNQFSWuyDuE9oEVP
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Decide number of sample
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Large sample data: good, credibility increases
$$$\bar{X} \pm z_{\frac{\alpha}{2}} \times \text{standard error} \\ $$$
$$$= \bar{X} \pm z_{\frac{\alpha}{2}} \times \frac{\sigma}{\sqrt{n}}$$$
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Simplify above equation with respect to n
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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
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confidence: 99%
z=2.58
allowed error += 100ml
d=100
population_std: 150ml
population_std=150
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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