This is personal study note
Copyright and original reference:
https://www.youtube.com/watch?v=N5cbASDXl1w&list=PLsri7w6p16vvQCo9pmuRNY_SYoOGB6bWM&index=3
================================================================================
002_002_Test_hypothesis_on_2_populations_mean_difference_with_independent_samples_Case1_enough_sample_in_same_population_variance_and_in_different_population_variance
================================================================================
================================================================================
Calculate confidence interval
================================================================================
Now, you should establish hypothesis
and then you should test the hypothesis
To do that, you should calculate test-statistic
================================================================================
================================================================================
Enough sample, no information about variance uniformity (general case)
- use sample variance
================================================================================
$$$H_0$$$: $$$\mu_A - \mu_B = 0$$$
Estimated one: $$$\bar{x}_A - \bar{x}_B$$$
$$$\sigma^2$$$ (population variance) is replaced with $$$s^2$$$ (sample variance)
================================================================================
What you want to estimate: $$$\mu_A-\mu_B$$$
$$$\bar{x}_A - \bar{x}_B$$$: alternatively you use mean difference of "sample"
Since it's sampe, you should use "interval" based on "given confidence interval"
================================================================================