Skewness is a measure of the asymmetry of a probability distribution about its mean. It quantifies the direction and extent of skew (departure from horizontal symmetry) in the data.

Frequentist statistics interprets probability as the long-run frequency of events, whereas Bayesian statistics interprets probability as a degree of belief or as subjective probability. The Bayesian approach uses Bayes' theorem to update probabilities based on new data.

Confidence intervals are used to estimate the range within which the true population parameter lies with a certain degree of confidence. They do not specifically determine the mean, median, or spread of a sample.

In a positively skewed distribution, the mean is greater than the median as the mean gets pulled in the direction of the skew (towards the right tail). In a negatively skewed distribution, the mean is less than the median as the mean gets pulled towards the left tail.

Non-parametric statistical methods do not require the data to follow a specific distribution, which is why they are often used when the assumptions of parametric tests are violated.

The peak of a distribution represents the mode of the data, that is, the value(s) that appear most frequently in the data set. In a perfectly symmetrical distribution, the mode, median, and mean coincide at the peak.

If we fail to reject the null hypothesis, this means that there is not enough evidence in the data to support the alternative hypothesis. We do not say the null hypothesis is true, because it is possible that a type II error (false negative) occurred.

In stratified sampling, the population is divided into non-overlapping groups, or strata, such as age groups, income levels, or gender. Then, a simple random sample is taken from each stratum. Stratified random sampling can provide more precise estimates if the strata are relevant to the characteristic of interest.

A low p-value in a t-test suggests that you can reject the null hypothesis. The p-value represents the probability that the results are due to random chance, so a lower p-value means the results are less likely to be due to chance.

Independence in probability theory refers to situations where the occurrence of one event does not affect the occurrence of another event. In other words, Events A and B are independent if the fact that A occurs does not affect the probability of B occurring.