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.

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 samples are randomly selected.

The two populations are not different.

The two populations have equal variances.

The means of the two populations are significantly different.

The populations have the same mean.

The populations follow a normal distribution.

The samples are dependent on each other.

The populations have equal variances.

I walked my dog today.

The sky is very blue!

Four people say Hello

We had pizza last night.

Determining if the data follows a normal distribution.

Calculating the mean of one population only.

Ensuring that one sample mean is larger than the other.

Collecting sample data from both populations.

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.