The following data is available for two independent samples :
| SAMPLE-1 | SAMPLE-2 | |
| sample size | 8 | 10 |
| sample mean | 191 | 199 |
| sample standard deviation | 10 | 12 |
Then the value of t-statistic is :
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → −1.54
For the difference of the means of two independent samples, the t-statistic divides the difference of the sample means by its standard error, built from the two sample variances:
\( \displaystyle t = \frac{\bar{x}_1 - \bar{x}_2}{\sqrt{\frac{s_1^2}{n_1} + \frac{s_2^2}{n_2}}} \)
Standard error:
\( \displaystyle \frac{s_1^2}{n_1} = \frac{100}{8} = 12.5, \quad \frac{s_2^2}{n_2} = \frac{144}{10} = 14.4 \)
\( \displaystyle \sqrt{12.5 + 14.4} = \sqrt{26.9} \approx 5.19 \)
Taking sample 1 first:
\( \displaystyle t = \frac{191 - 199}{5.19} = \frac{-8}{5.19} \approx -1.54 \)
The value is negative because the mean of sample 1 is the smaller one.
Note: This topic was not in the CUET 2026 syllabus.