Great effort, and I certainly hope more coders will get into statistics (most I know are only interested in machine learning). However, I think your definition of 1.3 "Confidence Interval around the Mean" could be improved. You state:
"A confidence interval reflects the set of statistical hypotheses that won't be rejected at a given significance level. So the confidence interval around the mean reflects all possible values of the mean that can't be rejected by the data."
That seems a bit vague and perhaps confusing. Might I suggest something more like this:
"The confidence interval specifies a range (+/- a multiple of the above standard error [SE]) around our estimate of the mean (x-bar) such that: if we repeated our sampling process an infinite number of times (i.e. with the same sample size and forming a new x-bar and SE each time [and therefore, a new confidence interval]), Confidence_Level% of those intervals would contain the population (true) mean."
In addition, I think in this case, at least, there are no assumptions about the data to worry about, given a sufficiently moderate sample size due to the Central Limit Theorem (I'm confident about that in the case of the mean (x-bar), but I'll leave it up to others to correct me if I'm wrong about this applying to the standard error (SE)).
"A confidence interval reflects the set of statistical hypotheses that won't be rejected at a given significance level. So the confidence interval around the mean reflects all possible values of the mean that can't be rejected by the data."
That seems a bit vague and perhaps confusing. Might I suggest something more like this:
"The confidence interval specifies a range (+/- a multiple of the above standard error [SE]) around our estimate of the mean (x-bar) such that: if we repeated our sampling process an infinite number of times (i.e. with the same sample size and forming a new x-bar and SE each time [and therefore, a new confidence interval]), Confidence_Level% of those intervals would contain the population (true) mean."
In addition, I think in this case, at least, there are no assumptions about the data to worry about, given a sufficiently moderate sample size due to the Central Limit Theorem (I'm confident about that in the case of the mean (x-bar), but I'll leave it up to others to correct me if I'm wrong about this applying to the standard error (SE)).