For each sample in List-I, the sample standard deviation s is calculated with divisor n − 1, and the t-statistic is \( t = \displaystyle\frac{\bar{x} - \mu_0}{s/\sqrt{n}} \).
Match List-I with List-II
| List-I (Sample) | List-II (Value of t) | ||
| (A) | n = 25, \(\bar{x} = 54\), s = 10, \(\mu_0 = 50\) | (I) | −2 |
| (B) | n = 16, \(\bar{x} = 47\), s = 8, \(\mu_0 = 50\) | (II) | 1.25 |
| (C) | n = 9, \(\bar{x} = 102.5\), s = 6, \(\mu_0 = 100\) | (III) | 2 |
| (D) | n = 4, \(\bar{x} = 29\), s = 3, \(\mu_0 = 32\) | (IV) | −1.5 |
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)-(II), (D)-(I)
In each case the standard error \(s/\sqrt{n}\) is found first, and then \(t = (\bar{x} - \mu_0) \div (s/\sqrt{n})\).
(A) n = 25, \(\bar{x} = 54\), s = 10, \(\mu_0 = 50\)
This matches (III) 2: \(s/\sqrt{n} = 10/5 = 2\), so t = 4 ÷ 2 = 2.
(B) n = 16, \(\bar{x} = 47\), s = 8, \(\mu_0 = 50\)
This matches (IV) −1.5: \(s/\sqrt{n} = 8/4 = 2\), so t = −3 ÷ 2 = −1.5.
(C) n = 9, \(\bar{x} = 102.5\), s = 6, \(\mu_0 = 100\)
This matches (II) 1.25: \(s/\sqrt{n} = 6/3 = 2\), so t = 2.5 ÷ 2 = 1.25.
(D) n = 4, \(\bar{x} = 29\), s = 3, \(\mu_0 = 32\)
This matches (I) −2: \(s/\sqrt{n} = 3/2 = 1.5\), so t = −3 ÷ 1.5 = −2.