This is personal study note
Copyright and original reference:
https://www.youtube.com/watch?v=iraPUcOH5uw&list=PLsri7w6p16vulKaxOlNQFSWuyDuE9oEVP&index=2
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Estimate "population's mean parameter in interval"
1. When you know "std parameter of population" (rare case)
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Example
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A_company
Estimate "mean lifespan of bulb" of population set
Extract 200 number of bulbs
sample_mean_lifespan=30000 hours
population_std=500 hours
Estimate "mean parameters interval" with 95% confidence (z=1.96)
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Calculation
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Standard deviation vs standard error
$$$ \text{std} = \sqrt{\text{variance}}$$$
standard error:
$$$\dfrac{\text{std from sample}}{\sqrt{n}}$$$
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Estimate population's mean parameter in interval
2. When you don't know std parameter of population (general case)
Use sample data's std
Since you don't know population's std, confidence interval becomes large
And you use t distribution (when you don't know population's parameters) than z distribution
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Example student heights
12 number students' height values
with 95% confidence, estimate population's mean parameter in interval
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Calculation
Sample mean and sample std
std error
degree of freedom = 12-1 =11
Estimate