In a Chi-square test for independence, the null hypothesis is always that the two variables are independent. This means that knowing the value of one variable does not help predict the value of the other variable.

The Central Limit Theorem allows us to make inferences about the Population based on sample data. It states that, with a large enough sample size, the sample mean will be normally distributed around the population mean. This enables us to estimate the parameters of the population and make predictions based on the sample data.

In probability theory, an experiment refers to a process or procedure that produces outcomes. The outcomes depend on chance or randomness. For example, tossing a coin or rolling a die is considered a random experiment because the outcome is not certain but depends on chance.

Mutually exclusive events are events that cannot occur at the same time - the occurrence of one event excludes the occurrence of the other(s). On the other hand, independent events are those where the occurrence of one event does not affect the probability of the occurrence of the other event(s). The concepts are related but distinct.

The two main types of data in statistics are Qualitative and Quantitative. Qualitative data, also known as categorical data, represents characteristics or attributes and cannot be mathematically quantified. Quantitative data, on the other hand, is numerical, representing measurements or counts that can be quantified mathematically.

A Type I error occurs when we reject the null hypothesis, even though it is true. This is also known as a "false positive" error.

In a t-test or Z-test, the p-value represents the probability of obtaining a sample statistic as extreme or more extreme than the observed statistic, assuming the null hypothesis is true.

It is more appropriate to use a two-way ANOVA instead of a one-way ANOVA when there are two independent variables. Two-way ANOVA is used to observe the interaction effect between the two independent variables on the dependent variable.

The Law of Large Numbers states that as a sample size grows, the sample mean will be closer to the population mean. This means that the larger the sample size, the more the sample mean approximates the population mean.

The Addition Rule in probability is used to calculate the probability that at least one of two (or more) events will occur. It states that the probability of the occurrence of at least one of two mutually exclusive events is the sum of their individual probabilities.

The primary purpose of an ANOVA (Analysis of Variance) test is to compare the means of three or more groups to see if they are different. It is a way to find out if survey or experiment results are significant. In other words, they help to figure out if you need to reject the null hypothesis or accept the alternate hypothesis.

To prevent overfitting, we can apply a technique called regularization in polynomial regression. Regularization involves adding a penalty term to the loss function during the process of training a model. This penalty term discourages the coefficients of the model from reaching large values, leading to a simpler model that's less likely to overfit.