CUET · MATHS · PYQ PAPER 2025

Consider the following hypothesis test :
\(H_0: \mu=15\)
\(H_a: \mu \neq 15\)
A sample of 50 provided a sample mean of 14.15 . If the sample standard deviation is 3 , then the value of the teat statistic in \(t\) - test is

A -1
B -2
C 1
D 2

Verified Solution

Answer & Solution

Correct Answer

(B) -2

Step-by-step Solution

Detailed explanation

\(t = \frac{\bar{x} - \mu_0}{s/\sqrt{n}}\) \(t = \frac{14.15 - 15}{3/\sqrt{50}}\) \(t = \frac{-0.85}{3/7.0710678}\) \(t = \frac{-0.85}{0.424264}\) \(t = -2.003\)

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

Same subject

Explore more questions on app

From CUET

Explore more questions on app

List-I	List-II
(A) \(\|A\|=0\)	(I) A is a symmetric matrix
(B) \(\|A\| \neq 0\)	(II) A is a skew-symmetric matrix
(C) \(A^T=A\)	(III) A is a singular matrix
(D) \(A^T=-A\)	(IV) A is a non-singular matrix

Consider the following hypothesis test :\(H_0: \mu=15\)\(H_a: \mu \neq 15\)A sample of 50 provided a sample mean of 14.15 . If the sample standard deviation is 3 , then the value of the teat statistic in \(t\) - test is

Step-by-step Solution

Consider the following hypothesis test :
\(H_0: \mu=15\)
\(H_a: \mu \neq 15\)
A sample of 50 provided a sample mean of 14.15 . If the sample standard deviation is 3 , then the value of the teat statistic in \(t\) - test is