Statistics & Applications

Inferential

Medium

applied

Which of the following is not correct about the Central Limit Theorem?

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

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

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

The sampling distribution of the sample mean approaches a Poisson distribution as the sample size gets larger.

✅ Correct Option: 4

The Central Limit Theorem (CLT) states that when many samples are taken and their averages calculated, those averages will form a bell-shaped (normal) distribution, regardless of the original data distribution.

Option 1 is correct.

The sampling distribution of the sample mean approaches a bell-shaped curve. This is exactly what the Central Limit Theorem describes - the pattern of sample averages always becomes bell-shaped.

Option 2 is correct.

A sample size of 30 or more is considered sufficient. This is the standard rule of thumb statisticians use. The guideline is $n \geq 30$ .

Option 3 is correct.

As sample size becomes larger, prediction becomes more accurate. Bigger samples provide more reliable information about the entire population.

Option 4 is incorrect.

The statement claims the sampling distribution approaches a Poisson distribution. This contradicts the Central Limit Theorem, which states the distribution becomes normal (bell-shaped), not Poisson.

The Central Limit Theorem always results in a normal distribution.

The answer is Option 4, as it incorrectly identifies the limiting distribution as Poisson rather than normal.

2025: 14 May Shift 1

Match List-I with List-II

List-I	List-II
(A) An observed set of population selected for analysis	(I) Parameter
(B) A specific characteristic of the population	(II) Hypothesis
(C) A specific characteristic of the sample	(III) Statistic
(D) A statement made about a population parameter for testing	(IV) Sample

Choose the correct answer from the options given below:

2025: 3 June Shift 1

Consider the following hypothesis

$H_0: \mu = 315$ and $H_a: \mu \neq 315$

A sample of 60 provided a sample mean of 324.6. The standard deviation ( $\sigma$ ) is 14 and level of significance $\alpha = 0.05$ . Then the confidence interval is:

[Given: $Z_{a/2}{\frac{14}{\sqrt60}} = 3.54$ ]

2025: 2 June Shift 1

A random sample of size 16 has 53 as mean. The sum of the squares of the deviations taken from mean is 150. If the population mean is 56 then the value of t-test statistic is:

2026: 22 May Shift 1

Which of the following are true ?

(A) If the mean of a normal variate is 12 and standard deviation is 4, then the Z-score of data point 20 is 2.

(B) Mean of the numbers obtained on throwing a die having '1' on three faces, '2' on two faces and '5' on one face is 3.

(D) For a binomial distribution, mean = 9 and the standard deviation is $\frac{3}{2}$ , then the number of trials is 12.

Choose the correct answer from the options given below:

2026: 29 May Shift 1

Consider the following hypothesis test:

$H_o: \mu \le 12$

$H_a: \mu > 12$

A sample of 25 provided a sample mean $\bar x=14$ and a sample standard deviation $s=4.32$ . The degree of freedom is

2025: 15 May Shift 2

A company 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 variance of 0.0004 cm². The value of test statistic is :

Which of the following is not correct about the Central Limit Theorem?

Solution

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