A Principal Component is a linear combination of the original features in a dataset. Each principal component is orthogonal to each other, meaning they are uncorrelated and each represents a different direction in which the data varies.

No, the Mann-Whitney U test is not used for paired samples. It is designed for two independent samples. For paired samples, a different test, such as the Wilcoxon signed-rank test, would be more appropriate.

The Mann-Whitney U test is more appropriate to use than a t-test when the data is not normally distributed. This test is a non-parametric alternative to the independent t-test and does not assume normality.

If the p-value is less than the chosen significance level in the Kruskal-Wallis Test, we reject the null hypothesis. It means there is enough evidence to suggest that at least one of the groups is different from the others.

The main difference between a population and a sample is that a sample is a subset of a population. A population refers to the entire group of individuals or observations that we're interested in, while a sample is a smaller group that's been selected from that population.

Increasing the sample size makes the test more sensitive, reducing both Type I and Type II errors. Similarly, a more stringent significance level (lower α) reduces the chance of a Type I error. However, it's important to note that decreasing Type I error probability often leads to an increase in Type II error probability, and vice versa. This is known as the Type I/Type II tradeoff.

The interquartile range (IQR) in a box plot represents the middle 50% of the data. It is the range within which the central half of the values fall and is calculated as the difference between the third quartile (Q3) and the first quartile (Q1).

In a positively skewed distribution, the mean is usually greater than the median. A positive skew means the right tail of the distribution is longer or fatter. The mean, being affected by the values of the data points, gets dragged in the direction of the tail, and hence is typically greater than the median in a positively skewed distribution.

A normal distribution, also known as Gaussian distribution, is symmetric and bell-shaped. It is characterized by its mean and standard deviation. The mean, mode and median are all equal and are located at the center of the distribution.

Nominal data is data that can be divided into categories but has no order or priority. It is a type of categorical data that simply allows us to classify or categorize. Examples include types of cuisine (Italian, Chinese, Mexican, etc.), hair color, or city of residence.