CUET Mathematics 2025 29 May Shift 2 PYQs

Let two independent random samples of sizes $n_1$ and $n_2$ respectively have been drawn from the same normal population. Let $\bar{x}_1$ and $\bar{x}_2$ be the means and let $s_1$ and $s_2$ be their standard deviations. In order to test whether the the two sample means $\bar{x}_1$ and $\bar{x}_2$ differ significantly or not, the t-test statistic is given by

Which of the following are correct?

(A) A statistical hypothesis is a statement about the population parameter which may be true or false.

(B) In a statistical hypothesis testing procedure, a Type I error is made when the null hypothesis is accepted when it is false.

(C) In a statistical hypothesis testing procedure, a Type II error is made when the null hypothesis is rejected when it is true.

(D) The number of degrees of freedom of a statistic is the number of independent variates used to compute that statistic.

Choose the correct answer from the options given below:

A random sample of 100 individuals provides 25 positive responses.

Then the point estimate of the population proportion with "positive" responses is: