For testing the difference between the means of two samples, the following data is available :
| Size | Mean | Variance | |
| Sample 1 | 5 | 40 | 101 |
| Sample 2 | 7 | 30 | 60 |
The value of the t0 - statistics is :
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → $10\sqrt{\frac{35}{1007}}$
To calculate the t-statistics,
$t_0=\frac{\bar{x_1}-\bar{x_2}}{\sqrt{\frac{{s_1}^2}{{n_1}^2}+\frac{{s_2}^2}{{n_2}^2}}}$
$=\frac{40-30}{\sqrt{\frac{101}{5}+\frac{60}{7}}}=10×\sqrt{\frac{35}{101×7+60×5}}$
$=10×\sqrt{\frac{35}{1007}}=10\sqrt{\frac{7}{222}}$