Resolved: Why are we considering the sample means in the denominator to calculate variance at 2.55?
Why do we have to consider the sample means in the denominator to calculate the variance at 2.55 in this case? Why not simply square the standard deviation to get the variance? Can someone please explain this? Thanks in advance.
Hello Debdeep!
Thanks for reaching out!
The reason we use this formula instead of simply squaring the standard deviations to get the variance is that we are dealing with two different populations (or groups) that may have different means and different variances. Therefore, we need to account for the variability within each group.
By using the formula in the video, we take into consideration both the spread of data within each group (standard deviations) and the potential difference between the means of the two groups. This allows us to construct a confidence interval that reflects the uncertainty associated with estimating the difference between the population means based on the samples.
In contrast, squaring the standard deviations and calculating the variance does not account for the fact that we are comparing two different groups or populations. It ignores the potential differences in means and treats both groups as if they were part of a single population. This approach would not provide a valid confidence interval for the difference between the means of the two independent groups.
Hope this helps!
Best,
The 365 Team