A simple random sample of five values 11, 5, 15, 7, 12 is taken from a population whose mean is 9. Match List-I with List-II.
| List-I | List-II | ||
| (A) | Sample mean | (I) | 4 |
| (B) | Point estimate of the population variance | (II) | 1 |
| (C) | Point estimate of the population standard deviation | (III) | 10 |
| (D) | Sampling error \(\bar{x} - \mu\) | (IV) | 16 |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → (A)-(III), (B)-(IV), (C)-(I), (D)-(II)
(A) Sample mean
\( \displaystyle \bar{x} = \frac{11 + 5 + 15 + 7 + 12}{5} = \frac{50}{5} = 10 \)
This matches (III) 10.
(B) Point estimate of the population variance
The deviations from 10 are 1, −5, 5, −3, 2, so
\(\sum (x - \bar{x})^2 = 1 + 25 + 25 + 9 + 4 = 64\)
The point estimate uses the divisor n − 1 = 4:
\( \displaystyle s^2 = \frac{64}{4} = 16 \)
This matches (IV) 16.
(C) Point estimate of the population standard deviation
\(s = \sqrt{16} = 4\)
This matches (I) 4.
(D) Sampling error \(\bar{x} - \mu\)
The sampling error is the sample mean minus the population mean:
\(10 - 9 = 1\)
This matches (II) 1.