Week 6 Test Feedback Comparing means from two sub-sample (e.g. weekly working hours, x, for males and females: • When comparing the two sample means, and testing whether they are likely to be drawn from distinct populations, we are testing whether the difference in sample means is close enough to zero to be caused by randomness. • This means we need to calculate a t-statistic for the difference , which is equal to the difference in the sample means ( ? 1 − ? 2 ) divided by the standard error (SE) for the difference = 𝑠 1 2 𝑛 1 + 𝑠 2 2 𝑛 2 . • Hence, when calculating the CI for the difference in sample means, we are calculating an “error margin” around the difference in sample means based on this SE. • So, for a 95% CI, it is ? 1 − ? 2 ± 1.96 𝑠 1 2 𝑛 1 + 𝑠 2 2 𝑛 2 . • We interpret this as: we can be 95% confident that the true difference in the population means 𝜇 2 − 𝜇 1 lies somewhere within that interval.