CUET Mathematics 2025 26 May Shift 2 PYQs

If $x_1, x_2, x_3, ..., x_n$ are n observations in a sample then which of following is/are TRUE?

(A) The mean $\bar{x}$ has n degree of freedom

(B) The mean $\bar{x}$ has (n-1) degree of freedom

(C) The standard deviation of the sample has (n-1) degree of freedom

(D) The standard deviation of the sample has n degree of freedom

Choose the correct answer from the options given below:

Consider the following hypothesis test:

$H_0: \mu \leq 12$

$H_a: \mu > 12$

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 $t = \frac{\bar{x} - \mu}{\frac{s}{\sqrt{n}}}$.

(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:

Which of the following are correct about t-test statistics?

(A) The mean of t-test distribution is 0.

(B) It depends on the degrees of freedom.

(C) It depends on population standard deviation.

(D) With more degrees of freedom, it closely resembles standard normal distribution.

Choose the correct answer from the options given below: