Question

Match List-I with List-II:

List-I	List-II
(A) Distribution of a sample leads to becoming a normal distribution	(I) Central Limit Theorem
(B) Some subset of the entire population	(II) Hypothesis
(C) Population mean	(III) Sample
(D) Some assumptions about the population	(IV) Parameter

Choose the correct answer from the options given below.

• (A) - (I), (B) - (II), (C) - (III), (D) - (IV)
• (A) - (I), (B) - (III), (C) - (IV), (D) - (II)
• (A) - (I), (B) - (II), (C) - (IV), (D) - (III)
• (A) - (III), (B) - (IV), (C) - (I), (D) - (II)

Hint:

In statistical analysis, understanding the key terms and their definitions is crucial for accurate interpretation. The Central Limit Theorem is a fundamental concept that explains how the distribution of the sample mean approximates normality as the sample size grows. Additionally, remember that a hypothesis is tested to make inferences about a population, and parameters like the population mean are characteristics of the entire population. Matching concepts to definitions will help clarify their application in statistics.

Answer 1

The Correct Option is B

To solve the problem of matching List-I with List-II, we must understand each term mentioned in the lists:

1. Central Limit Theorem: This theorem states that when a sample is drawn from a population, the sample's distribution will approximate a normal distribution as the sample size becomes large. Therefore, "Distribution of a sample leads to becoming a normal distribution" matches with Central Limit Theorem (I).
2. Sample: A sample refers to any subset of the entire population used for analysis. Hence, "Some subset of the entire population" corresponds to Sample (III).
3. Parameter: A parameter is a numeric characteristic of a population, such as a mean or variance. Thus, "Population mean" is a Parameter (IV).
4. Hypothesis: This involves forming assumptions about a population that can be tested, leading to "Some assumptions about the population" matching with Hypothesis (II).

Therefore, the correct matches are as follows:

List-I	List-II
(A) Distribution of a sample leads to becoming a normal distribution	(I) Central Limit Theorem
(B) Some subset of the entire population	(III) Sample
(C) Population mean	(IV) Parameter
(D) Some assumptions about the population	(II) Hypothesis

The correct option is: (A) - (I), (B) - (III), (C) - (IV), (D) - (II).

Answer 2

Let us analyze each statement from List-I and match it with the appropriate option in List-II:

The Central Limit Theorem (I) is a fundamental concept in statistics. It states that, for a large enough sample size, the sampling distribution of the sample mean will approach a normal distribution, regardless of the original distribution of the population. This is important because it allows statisticians to make inferences about population parameters using sample statistics, even if the population distribution is not normal.

A Sample (III) refers to a subset of individuals or observations selected from a larger population. It is used to gather information and make inferences about the entire population. Since it is not always feasible to study an entire population, a sample serves as a practical and efficient alternative for drawing conclusions about the population.

The Population Mean (IV) is a parameter that represents the average of all values in a population. Unlike a sample mean, which is based on a subset of the population, the population mean is fixed and unchanging, making it a characteristic of the entire population. The population mean is often denoted by \( \mu \), and is used as a reference point for making statistical analyses.

A Hypothesis (II) refers to an assumption or claim about the population or a process that can be tested using statistical methods. Hypothesis testing involves determining whether there is enough evidence in a sample to support or reject a hypothesis about a population parameter. This is fundamental to inferential statistics, as it helps in drawing conclusions from sample data.

Thus, the correct matching is:

\( (A) - (I), (B) - (III), (C) - (IV), (D) - (II) \).