Statistics & Applications

Inferential

Medium

applied

Which of the following are correct?

(A) The probability curve in t-distribution is symmetric about the line t=0.

(B) t-axis is an asymptote of the curve.

(C) The variable t of t-distribution ranges from $-\infty$ to $\infty$

(D) As the number of degrees of freedom increases, the t-distribution curve moves closer to the binomial distribution.

Choose the correct answer from the options given below:

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

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

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

✅ Correct Option: 1

The probability curve in t-distribution is symmetric about the line $t=0$ .

The t-distribution is centered at zero with mean $= 0$ . The curve is perfectly balanced on both sides, with the left and right halves being mirror images of each other.

Statement (A) is correct.

The t-axis is an asymptote of the curve.

As $t \to -\infty$ or $t \to +\infty$ , the curve approaches the horizontal t-axis but never touches it. The probability never becomes exactly zero.

Statement (B) is correct.

The variable $t$ of t-distribution ranges from $-\infty$ to $\infty$ .

The t-value can be any real number from negative infinity to positive infinity. There is no upper or lower limit to possible t-values, though extreme values are very rare.

Statement (C) is correct.

As the number of degrees of freedom increases, the t-distribution curve moves closer to the binomial distribution.

As degrees of freedom increase, the t-distribution approaches the normal distribution, not the binomial distribution. The normal distribution is continuous and bell-shaped, while the binomial distribution is discrete.

Statement (D) is incorrect.

Statements (A), (B), and (C) are correct.

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: 22 May Shift 1

Which one of the following statement is not correct?

2026: 12 May Shift 2

Match List-I with List-II

List-I (Types of Probability Sampling)	List-II (Characteristic)
(A) Simple random sampling	(I) Every member of the population is arranged in a particular order. The first member is selected at random and then the remaining members are selected at regular intervals.
(B) Systematic sampling	(II) The population is divided into subgroups and each subgroup has similar characteristics of the whole population.
(C) Stratified sampling	(III) Every member of the population has an equal chance of being selected.
(D) Cluster Sampling	(IV) The population is divided into subgroups based on the relevant characteristics

Choose the correct answer from the options given below:

2024: 16 May Shift 1

The following data is from a simple random sample :

$15,23, x, 37,19,32$

If the point estimate of the population mean is $23$ , then the value of $x$ is :

2025: 26 May Shift 2

Consider the following test:

H₀: μ ≤ 12

H₁: μ > 12

A sample of 36 provided a sample mean $\bar{x} = 16$ and a sample standard deviation S=4.2. Then the value of the t- test statistic is:

2025: 3 June Shift 2

For the following data:

	Size	Mean	Standard deviation
Sample 1	4	40	8
Sample 2	5	50	10

The sample statistic t follows t-distribution with 'm' degrees of freedom, then m is equal to

Solution

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