A random sample of 16 observations has mean 52 and \(\sum (x - \bar{x})^2 = 960\). The sample standard deviation is taken as \(s = \sqrt{\displaystyle\frac{\sum (x - \bar{x})^2}{n - 1}}\), and the test value is \(\mu_0 = 49\).
Match List-I with List-II
| List-I (Quantity) | List-II (Value) | ||
| (A) | Degrees of freedom | (I) | 1.5 |
| (B) | Sample standard deviation s | (II) | 2 |
| (C) | Standard error \(s/\sqrt{n}\) | (III) | 8 |
| (D) | Value of the t-statistic | (IV) | 15 |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → (A)-(IV), (B)-(III), (C)-(II), (D)-(I)
Here n = 16, \(\bar{x} = 52\) and \(\mu_0 = 49\).
(A) Degrees of freedom
This matches (IV) 15: df = n − 1 = 16 − 1 = 15.
(B) Sample standard deviation s
This matches (III) 8:
\( \displaystyle s = \sqrt{\frac{960}{15}} = \sqrt{64} = 8 \)
(C) Standard error \(s/\sqrt{n}\)
This matches (II) 2: \(8/\sqrt{16} = 8/4 = 2\).
(D) Value of the t-statistic
This matches (I) 1.5:
\( \displaystyle t = \frac{52 - 49}{2} = 1.5 \)