CUET Mathematics - When the two independent small samples of sizes n_1 and n_2 with means x_1 and x_2 respectively are drawn from populations with identical population variances, the test-statistic is computed as | PYQs + Solutions

CUET Mathematics 2025 13 May Shift 2

Statistics & Applications

Easy

applied

$t = \frac{\bar{x}_1 - \bar{x}_2}{S_p\sqrt{\frac{1}{n_1} + \frac{1}{n_2}}}$ , where $S_p$ is pooled standard deviation.

$t = \frac{\bar{x}_1 - \bar{x}_2}{S_p\sqrt{\frac{1}{n_1} - \frac{1}{n_2}}}$ , where $S_p$ is pooled standard deviation.

$t = \frac{\bar{x}_1 + \bar{x}_2}{S_p\sqrt{\frac{1}{n_1} - \frac{1}{n_2}}}$ , where $S_p$ is pooled standard deviation.

$t = \frac{\bar{x}_1 + \bar{x}_2}{\sqrt{\frac{1}{n_1} - \frac{1}{n_2}}}$ , where $S_p$ is pooled standard deviation.

✅ Correct Option: 1

Related questions:

3 June Shift 2

Which of the following statements are TRUE?

(A) The variable t of t-distribution ranges from $-\infty$ to $\infty$ .

(B) The probability curve of the t-distribution is symmetric about the line $t=0$

(D) As the number of degrees of freedom decreases, the t-distribution curve moves closer to the standard normal probability curve.

Choose the correct answer from the options given below:

22 May Shift 1

Consider the following hypothesis test:

$H_0: \mu \leq 16$

$H_a: \mu > 16$

A sample of 25 provided a sample mean $\bar{x} = 17$ and a sample standard deviation $s = 3.5$ , then the value of the test statistic in $t$ -test is:

CUET Mathematics 2024 Slot 1

If $95 \%$ confidence interval for the population mean was reported to be $160$ to $170$ and $\sigma=25$ , then size of the sample used in this study is: (Given $\mathrm{Z}_{0.025}=1.96$ )

CUET Mathematics 2025 13 May Shift 2 PYQs

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