The Law of Large Numbers has many practical applications. For example, insurance companies use it to predict future claim amounts. The law allows them to predict losses and to set premiums in a way that ensures profitability, by basing predictions on large aggregations of independent or nearly independent losses.

If a confidence interval for a mean difference or an effect size includes zero, it suggests that there is no effect in the population and that the observed effect in the sample is likely due to sampling error.

A suitable data transformation may make it possible to use a parametric test instead of a non-parametric test. Transformations can help to stabilize variances, normalize the data, or linearize relationships between variables, allowing for the use of parametric tests that might have more statistical power.

Heteroscedasticity, or non-constant variance of the error term, can invalidate statistical inferences that could be made from the model because it violates one of the assumptions of multiple linear regression. This could lead to inefficient estimation of the regression coefficients and incorrect standard errors, which in turn affects confidence intervals and hypothesis tests.

In PCA, if two variables are similar or highly correlated, they will have high loadings on the same component. This is because PCA identifies the directions (Principal Components) in which the data varies the most, and similar variables will contribute to this variance in the same way.

The bin width and the number of bins in a histogram can dramatically affect the interpretation, skewness, and overall appearance of the histogram. This is because the choice of bin size can influence the level of detail visible in the histogram, potentially either obscuring or highlighting certain patterns in the data.

The elbow method involves plotting the explained variation as a function of the number of clusters and picking the elbow of the curve as the number of clusters to use. This 'elbow' is the point representing the optimal number of clusters at which the within-cluster sum of squares (WCSS) doesn't decrease significantly with each iteration.

A VIF greater than 5 is often taken as an indication of high multicollinearity among the predictors in a regression model. This could lead to imprecise and unreliable estimates of the regression coefficients.

The mode can be misleading or irrelevant especially with continuous data. Since the mode is the most frequently occurring value, with continuous data the frequency of each value is often the same (i.e., 1), hence it becomes difficult to define a mode in a traditional sense.

A Type II error, also known as a false negative, occurs when the null hypothesis is false, but we fail to reject it.

If two events are independent, the conditional probability of one event given the other is simply the probability of the event itself. This is because in independent events, the occurrence of one event does not affect the occurrence of the other event.

The range of a dataset is sensitive to outliers. Because the range is calculated as the difference between the maximum and minimum values, an outlier (an extremely high or low value) can greatly increase the range.