CUET · MATHS · PYQ PAPER 2025
When two independent small samples of sizes \(n_1\) and \(n_2\) with means \(\bar{x}_1\) and \(\bar{x}_2\) respectively are drawn from populations with identical population variances, the test-statistic is computed as :
- A \(t=\frac{\bar{x}_1-\bar{x}_2}{S_p \sqrt{\frac{1}{n_1}+\frac{1}{n_2}}}\), where \(S_p\) is pooled standard deviation.
- B 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.
- C 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.
- D t \(=\frac{\bar{x}_1+\bar{x}_2}{\sqrt{\frac{1}{n_1}-\frac{1}{n_2}}}\), where \(S_p\) is pooled standard deviation.
Answer & Solution
Correct Answer
(A) \(t=\frac{\bar{x}_1-\bar{x}_2}{S_p \sqrt{\frac{1}{n_1}+\frac{1}{n_2}}}\), where \(S_p\) is pooled standard deviation.
Step-by-step Solution
Detailed explanation
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.
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