Applied Mathematics

Inferential Statistics

Medium

applied

From a sample of 5 items having values 2, 4, 6, 7, 6, the unbiased estimates of the population mean and the standard deviation are:

5, $\sqrt{2}$

5, $\frac{\sqrt{2}}{2}$

$\sqrt{5}$ , 2

5, 2

✅ Correct Option: 4

Mean $\bar{x} = \frac{2+4+6+7+6}{5} = 5$ .

Deviations from mean: $-3, -1, 1, 2, 1$ . Squared: $9, 1, 1, 4, 1$ , sum $= 16$ .

Unbiased variance $s^2 = \frac{16}{n-1} = \frac{16}{4} = 4$ . So $s = 2$ .

2023: 22 May Shift 3

The assumption opposite of what is made in the null hypothesis is known as the _________ hypothesis.

2023: 22 May Shift 3

Match List - I with List - II.

	List - I		List - II
(A)	Left tailed test	(I)	$H_0 : \mu = 50$
(B)	Two tailed test	(II)	$H_1 : \mu > 50$
(C)	Null hypothesis	(III)	$H_1 : \mu < 50$
(D)	Right tailed test	(IV)	$H_1 : \mu \neq 50$

Choose the correct answer from the options given below :

2026: 29 May Shift 2

A simple random sample consists of five observations: 2, 4, 6, 7,11, then which of the following are true ?

A. Sample mean = 7.5

B. Sample mean = 6

C. Sample standard deviation = $\sqrt{11}$

D. Sample standard deviation = $\sqrt{11.5}$

Choose the correct answer from the options given below:

2026: 14 May Shift 2

Five students are selected at random from a school and their weights are found to be 50, 51, 53, 54 and 62. The point estimation of the population mean is:

2023: 15 June Shift 2

Match List - I with List - II.

List - I	List - II
(A) A special characteristic of a population is called	(I) Sample Size
(B) The number of statistical individuals in a sample is called	(II) Statistic
(C) A special characteristic of a sample is called	(III) Standard error
(D) The standard deviation of the sampling distribution of a statistic is known as its	(IV) Parameter

Choose the correct answer from the options given below :

2023: 7 June Shift 1

Which of the following is not a statistic ?

From a sample of 5 items having values 2, 4, 6, 7, 6, the unbiased estimates of the population mean and the standard deviation are:

Solution

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