Means

Paired t-test because it compares means from related samples on same subjects before and after an intervention.

Chi-square goodness-of-fit test to see if actual pre- and post-scores match expected frequencies based on teaching methods used.

ANOVA (Analysis Of Variance) as it compares more than two groups' means simultaneously assessing overall significance only.

Independent samples t-test since students acted as their own control group during testing periods.

The test incorrectly suggests that larger standard deviations necessitate non-parametric methods irrespective-of actual distribution shapes observed among datasets analyzed previously elsewhere before now too sometimes perhaps occasionally maybe potentially hypothetically conceivably perchance once-or-twice every-so-often now-and-then...

Passing implies robustness against outliers that could skew inferential accuracy otherwise unaccounted-for by traditional methods alone

Failure indicates non-normality even if underlying distributions meet requirements due-to sampling fluctuations

Low statistical power makes Shapiro-Wilk less reliable at detecting departures from normality with small samples.

The null hypothesis is definitely false beyond any possible doubt.

A Type I error has been committed as per significance level determined.

There is no difference between the two population means being compared.

The data provide sufficient evidence to reject the null hypothesis.

To calculate the effect size of the difference

To determine the significance level for the test

To ensure valid results and avoid misinterpretation

To assess the homogeneity of variances

Use only the largest standard deviation out of the two samples to calculate confidence intervals for comparison.

Imply calculations that eliminate the need to consider individual group variances in complex models.

Estimate the common measure of spread across the combined samples when the populations are assumed to have equal variances.

Assess overall variability between groups to determine whether treatment effects are present or not.

It could potentially decrease type II errors by providing a more accurate estimation without relying on normality assumptions.

Bootstrapping affects only type I errors while leaving type II error probabilities unaffected by changes in distribution shape.

Non-normality invalidates bootstrap results entirely thus inflating both types I and II errors indiscriminately due to model misspecification.

Bootstrapping will generally increase type II errors due to overfitting data from resampling techniques used in this method.

The samples' means

The samples' minima

The samples' modes

The samples' sums

One sample has much greater variance than the other sample.

Both samples are random and drawn independently from each other.

Both samples come from populations with normal distributions.

Sample sizes are large enough for Central Limit Theorem to apply to distribution approximations.

Carefully measuring more control variables can reduce variability but not precisely estimate the mean difference necessarily

Optimizing the measurement techniques may enhance the quality of data without directly improving the precision in the difference

Larger sample size will reduce margins of error and improve precision in the difference estimate between population means

The implementation of stringent control measures ensures greater precision in measuring the differences

The populations from which the samples were taken must be normally distributed or large enough for normal approximation.

The data must come from matched or paired observations.

The sample sizes must be equal between both groups.

The populations from which the samples are drawn have dependent distributions.