Standard error
The estimated standard error for the two-sample T-interval is the same formula we used for the two-sample T-test.
Standard error is given by the formula\[ \sqrt{{\frac{s_1^2}{n_1}+\frac{s_2^2}{n_2}}}\]
where s1 and s2denote the sample standard deviations
and n1 and n2 denote the sample sizes
For example
| sample no |
Size |
mean |
Std deviation |
| Sample 1 |
45 |
850 |
252 |
| Sample 2 |
27 |
719 |
322 |
here \[s_1^2=252^2\]
\[s_2^2=322^2\]
\[n_1=45\]
\[n_2=27\]
putting all of these in formula \[ \sqrt{{\frac{252^2}{45}+\frac{322^2}{27}}}=72.47\]
Assumptions in the calculation block
\[r=s_1\]
\[s=s_2\]
\[n=n_1\]
\[m=n_2\]
Boundary conditions
\[n_1\] ,\[n_2\] \[\geqslant \] 30
