Statistics & Applications

Inferential

Medium

applied

Which of the following are correct?

(A) A statistical hypothesis is a statement about the population parameter which may be true or false.

(B) In a statistical hypothesis testing procedure, a Type I error is made when the null hypothesis is accepted when it is false.

(C) In a statistical hypothesis testing procedure, a Type II error is made when the null hypothesis is rejected when it is true.

(D) The number of degrees of freedom of a statistic is the number of independent variates used to compute that statistic.

Choose the correct answer from the options given below:

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

(A) and (D) only

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

(B) and (C) only

✅ Correct Option: 2

Statement (A): A statistical hypothesis is a statement about the population parameter which may be true or false.

This statement is correct. A hypothesis is a claim about a population parameter (like average height, proportion of voters, etc.) that can either be true or false until tested.

Statement (B): In a statistical hypothesis testing procedure, a Type I error is made when the null hypothesis is accepted when it is false.

This statement is incorrect.

Type I Error occurs when the null hypothesis is rejected when it is actually true (false alarm).

Type II Error occurs when the null hypothesis is accepted when it is actually false (missed detection).

Statement B describes Type II error, not Type I error.

Statement (C): In a statistical hypothesis testing procedure, a Type II error is made when the null hypothesis is rejected when it is true.

This statement is incorrect.

Statement C describes Type I error, not Type II error. The definitions are reversed.

Statement (D): The number of degrees of freedom of a statistic is the number of independent variates used to compute that statistic.

This statement is correct. Degrees of freedom (df) represents the number of independent pieces of information available to compute a statistic.

For example, if there are 10 numbers with a known average, only 9 are free to vary (the 10th is fixed), so df $= n - 1 = 9$ .

Only statements (A) and (D) are correct.

Therefore, the answer is Option 2.

2025: 15 May Shift 2

Let two independent random samples of sizes $n_1$ and $n_2$ respectively have been drawn from the same normal population. Let $\overline{X_1}$ and $\overline{X_2}$ be the means and let $s_1$ and $s_2$ be their standard deviations. In order to test whether the the two sample means $\overline{X_1}$ and $\overline{X_2}$ differ significantly or not, the $t$ -test statistic is given by

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:

2025: 15 May Shift 1

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

2026: 18 May Shift 1

If we reject the null hypothesis when it is true, we might be making

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:

Solution

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