Match List - I with List - II.
| List - I | List - II | ||
| (A) | t-distribution | (I) | sample size \(\ge 30\) |
| (B) | Sample mean | (II) | \(\overline{\mathrm{X}}\) |
| (C) | Population mean | (III) | degree of freedom |
| (D) | Z-distribution | (IV) | \(\mu\) |
Choose the correct answer from the options given below :
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → (A)-(III), (B)-(II), (C)-(IV), (D)-(I)
(A) t-distribution
This matches (III) degree of freedom.
The shape of the t-distribution depends on its degrees of freedom (n − 1 for one sample).
(B) Sample mean
This matches (II) \(\overline{\mathrm{X}}\).
The mean of a sample is written \(\overline{X}\).
(C) Population mean
This matches (IV) \(\mu\).
Parameters of the population are written with Greek letters; the population mean is \(\mu\).
(D) Z-distribution
This matches (I) sample size \(\ge 30\).
For a large sample (30 or more), the sample mean is close to normal, so the Z (standard normal) test is used.