In a 95% confidence interval, if the true population parameter lies outside of the interval, it is considered a Type I error. This is when the null hypothesis is true, but is incorrectly rejected.

PCA reduces the dimensionality of a dataset by creating new uncorrelated variables that successively maximize variance. These new variables or "principal components" can replace the original variables, thus reducing the data's dimensionality.

A Chi-square test for independence is used to determine if there is a significant relationship between two categorical variables. It is not applicable for continuous, ordinal, or nominal variables.

By definition, the probability of an event is a number between 0 and 1. A probability of 0 means the event will never occur, and a probability of 1 means the event is certain to occur.

In a Chi-square test, having small expected frequencies can reduce the power of the test and potentially lead to erroneous conclusions. This is because the Chi-square test is based on the assumption that the expected frequency of each category is at least 5.

The standard error plays a crucial role in interval estimation. It is used to calculate the margin of error, which determines the width of the confidence interval. The standard error measures the variability of the sample mean around the population mean. A smaller standard error will result in a narrower confidence interval, assuming the confidence level is constant.

Spearman's Rank Correlation is a non-parametric method, which means it does not make assumptions about the distribution of data. This makes it more flexible and robust than some parametric methods.

The Central Limit Theorem generally applies when the following conditions are met: 1) The data should be sampled randomly, 2) The sample values must be independent of each other, and 3) The sample size should be sufficiently large (typically, n > 30 is considered sufficient).

A Type II error, also known as a false negative, occurs when we fail to reject a false null hypothesis. This means we've missed evidence of an effect or difference that truly exists.

Pearson's correlation coefficient measures linear relationships between variables. It measures the degree to which pairs of data for these two variables lie on a line.