Assertion (A) is correct because of the Law of Large Numbers. However, Reason (R) is incomplete because the Law of Inertia of Large Numbers is only one aspect; sampling theory also relies on the Law of Statistical Regularity and the Central Limit Theorem to ensure representativeness in random sampling.

Non-parametric tests do not assume a normal distribution of the data. The Mann-Whitney U test, Kruskal-Wallis test, and Chi-square test are classic examples of non-parametric methods. Conversely, the F-test and T-test are parametric tests that rely on assumptions about population parameters and normal distribution.

Systematic sampling is a type of probability sampling where elements are selected from a population at a regular interval (k). Because every member of the population has a known, non-zero chance of being selected, it is strictly categorized as a probability sampling technique, distinct from non-probability methods like quota sampling.

Statement I is incorrect because rejecting a true null hypothesis is a Type I error, not Type II. Statement II is incorrect because the z-test requires a large sample size or a known population standard deviation; for small samples with unknown population standard deviation, the t-test is the appropriate statistical tool. Since both statements contain fundamental errors in statistical theory, option B is the correct choice.

Level of significance relates to Type I error (a-3). The standard deviation of a sampling distribution is known as the standard error (b-4). A numerical value describing a population is a parameter (c-2). A normally distributed population is often assumed when the sample mean equals the population mean in specific tests (d-1).

The power of a test is the probability of rejecting a false null hypothesis. Type II error is accepting a false null hypothesis. Level of significance is the probability of rejecting a true null hypothesis. Type I error is rejecting a true null hypothesis.

Parametric tests are generally preferred as the first choice in statistical analysis because they have higher statistical power when assumptions are met. Non-parametric tests are often used as alternatives when data does not meet these assumptions, and they are frequently cited as being computationally simpler and less demanding regarding data distribution requirements.

Statement I is false because non-parametric tests are 'distribution-free' and do not assume a specific population distribution. Statement II is true, as the standard deviation of a sampling distribution of the mean is defined as the standard error of the mean.

The Chi-square statistic is calculated using the formula Σ((O-E)² / E). By calculating the squared difference between observed and expected frequencies for each category and dividing by the expected frequency, the sum yields approximately 6.76.

In statistics, the 'universe' or 'population' refers to the entire group of individuals or items under study. A sample is a smaller, selected group intended to represent the characteristics of this entire population. By analyzing the sample, researchers draw inferences about the larger universe from which it was drawn.