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CUET · MATHS · PYQ PAPER 2025

Consider the following hypothesis test:
\( \begin{array}{l} H_0: \mu \leq 12 \\ H_a: \mu>12 \end{array} \)
A sample of 25 provided a sample mean \(\bar{x}=14\) and a sample standard deviation \(S=4.32\). If \(t_{0.05}=1.711\), then which of the following is correct?
(A) The test statistic is defined as \(t=\frac{\bar{x}-\mu}{S / \sqrt{n}}\).
(B) The value of the test statistic is 1.31 .
(C) At \(\alpha=0.05\), the null hypothesis is rejected.
(D) If the value of the \(t\)-statistic is less than \(t_\alpha\), then null hypothesis is accepted.
Choose the correct answer from the options given below:

  1. A (A), (B) and (C) only
  2. B (B), (C) and (D) only
  3. C (A), (C) and (D) only
  4. D (A) and (D) only
Verified Solution

Answer & Solution

Correct Answer

(C) (A), (C) and (D) only

Step-by-step Solution

Detailed explanation

\( t = \frac{\bar{x}-\mu}{S / \sqrt{n}} \) \( t = \frac{14-12}{4.32 / \sqrt{25}} = \frac{2}{4.32/5} = \frac{2}{0.864} \approx 2.31 \) (A) is correct; (B) is incorrect (\( 2.31 \neq 1.31 \)); (C) is correct (\( 2.31 > 1.711 \), reject \( H_0 \)); (D) is correct. (A), (C) and (D)…