Question : Consider a random sample of 10 patients using a drug A for headache remedy yields sample mean and variance as 12.3 minutes and 6.54 minutes, while a random sample of 10 other patients using drug B gives sample mean and variance as 10.1 minutes and 4.1 minutes. Find a 95% confidence interval for the true difference in the mean relief times.

--------------------------My work ---------------------------

$\displaystyle n_1 = 10 $

$\displaystyle \bar x_1 = 12.3$

$\displaystyle \sigma^2 _1 = 6.54$

$\displaystyle n_2 = 10 $

$\displaystyle \bar x_2 = 10.1$

$\displaystyle \sigma^2 _2 = 4.1$

$\displaystyle \alpha$ = 0.05 degree of freedom = 0.95

$\displaystyle t = \frac{x_1 - x_2}{\sqrt{\frac{\sigma^2 _ 1}{n_1} + \frac{\sigma^2 _2}{n_2}}}$

Is this correct what i am trying to do ???