Statistics & Applications

Inferential

Medium

applied

Which of the following statements are correct about the "Central Limit Theorem"?

(A) The sampling distribution of the sample mean approaches the normal distribution as the sample size gets larger.

(B) A sample size of 30 or more is considered to be sufficient to hold the "Central Limit Theorem".

(C) As the sample size becomes larger, the prediction of characteristics of the population becomes more accurate.

(D) The sampling distribution of the sample mean approaches a bell shaped curve as the sample size gets larger.

Choose the correct answer from the options given below:

(A), (B) and (D) only

(A), (B) and (C) only

(A), (B), (C) and (D)

✅ Correct Option: 3

The Central Limit Theorem states that the sampling distribution of the sample mean approaches the normal distribution as the sample size gets larger. This fundamental principle applies regardless of the original population distribution.

Statement (A) is correct. The sampling distribution of the sample mean approaches the normal distribution as the sample size increases. Even if the original data has a non-normal distribution, the distribution of sample means becomes normally distributed with larger sample sizes.

Statement (B) is correct. A sample size of 30 or more is considered sufficient for the Central Limit Theorem to hold. This is a widely accepted practical guideline in statistics, where $n \geq 30$ is the standard threshold.

Statement (C) is correct. As the sample size becomes larger, the prediction of population characteristics becomes more accurate. Larger samples provide more information about the population, resulting in estimates closer to true population values with smaller margins of error.

Statement (D) is correct. The sampling distribution of the sample mean approaches a bell-shaped curve as the sample size gets larger. A bell-shaped curve is the characteristic shape of a normal distribution, making this statement equivalent to statement (A).

All four statements (A), (B), (C), and (D) are correct descriptions of the Central Limit Theorem.

Therefore, the correct answer is: (A), (B), (C) and (D)

2025: 16 May Shift 1

A machine has been producing steel tubes of mean inner diameter of 2 cm. A sample of 10 tubes gives an inner diameter of 2.01 cm and a standard deviation of 0.063 cm. Test the hypothesis that the machine is working in the proper order at 5 % level of significance and answer, which of the following statements are correct?

[Given that : t₉(0.05) = 2.262]

(A) The value of the test statistic is t = 0.476.

(B) The null hypothesis is rejected at 5 % level of significance.

(D) The degree of freedom is 10.

Choose the correct answer from the options given below:

2025: 13 May Shift 2

Arrange the following as per statistical inferences:

(A) Data Analysis

(B) Population

(D) Data Collection

Choose the correct answer from the options given below:

2025: 2 June Shift 1

For 95% confidence interval for a population mean reported to be 132 to 142 with standard deviation $\sigma = 17.85$ then the sample size used in this case, is:

[Given that: $Z_{0.125} = 1.96$ ]

2025: 22 May Shift 1

Consider the following hypothesis test:

$H_0: \mu \leq 16$

$H_a: \mu > 16$

A sample of 25 provided a sample mean $\bar{x} = 17$ and a sample standard deviation $s = 3.5$ , then the value of the test statistic in $t$ -test is:

2025: 26 May Shift 2

The point estimate of the population standard deviation as per the below mentioned data from a simple random sample 6,10,15,12,9,8 will be :-

2026: 18 May Shift 1

Which of the following statements are correct?

(A) A sample size of 30 or more is considered to be sufficient to hold the central limit theorem.

(B) A survey done using a sample of the population has no margin of error.

(D) The sample makes an inference about the population.

Choose the correct answer from the options given below:

Solution

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