The sampling distribution of the sample mean approaches a normal distribution as the sample size gets larger, no matter what is the shape of the population distribution. The above statement is: Option 1: Fundamental sampling theorem Option 2: Central limit theorem Option 3: Hypothesis testing process Option 4: Inferential statistical theorem

Answer: Central limit theorem. Solution: The statement describes exactly the Central Limit Theorem: for large n, the sampling distribution of X tends to normality regardless of the parent population's shape. This is why normal-based inference works even for non-normal populations when samples are large.

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The sampling distribution of the sample mean approaches a normal distribution as the sample size gets larger, no matter what is the shape of the population distribution.

The above statement is:

Fundamental sampling theorem

Central limit theorem

Hypothesis testing process

Inferential statistical theorem

✅ Correct Option: 2

The statement describes exactly the Central Limit Theorem: for large $n$ , the sampling distribution of $\bar X$ tends to normality regardless of the parent population's shape.

This is why normal-based inference works even for non-normal populations when samples are large.

2026: 18 May Shift 1

Consider the following hypothesis test:

$H_0: \mu \leq 25$

$H_a: \mu > 25$

A sample of 25 provided a sample mean of 27.80. The population standard deviation is 5, then the value of the test statistic is

2026: 29 May Shift 1

Which of the following are correct?

(A) The central limit theorem (CLT) states that the sampling distribution of the sample approaches a normal distribution as the sample size gets larger, no matter what is the shape of the population distribution.

(B) The measurable characteristic of population is called parameter.

(D) The sample makes inference about the population.

Choose the correct answer from the options given below:

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:

2026: 22 May Shift 1

In a confidence interval, the range of values above and below the sample statistic is called :

2025: 3 June Shift 1

A small start-up started making wafers and distributing them to the retailers. After a week, average sales per week were found to be 150 packets. So, to increase the sales, a strategy was used to change the packaging and add a chocolate worth Rs. 5 as a free gift with the pack. After this, a sample of 17 shops was taken, which showed that sales went up with mean 165 and a standard deviation of 25. Check whether the strategy was effective @5%, level of significance ? [Given $t_{16} (0.05) =2.12$ ]

2026: 21 May Shift 1

A sample of size 9 from a normal population with sample mean $\bar{X} = 15.8$ and population estimated standard deviation $\sigma = 3.21$ , then 99% confidence interval for population mean is : $(Use: t_8(0.01) = 3.335)$

The sampling distribution of the sample mean approaches a normal distribution as the sample size gets larger, no matter what is the shape of the population distribution. The above statement is:

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CUET Mathematics Past Year Questions (Topic-Wise)

The sampling distribution of the sample mean approaches a normal distribution as the sample size gets larger, no matter what is the shape of the population distribution.

The above statement is: