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" ================================================================================