Hypothesis testing question

Previous research has indicated that changes in the activity of dopamine may be a contributing factor to schizophrenia. The dopamine levels among 11 patients classified as suffering from psychosis and 11 that aren't are measured and give the following statistics respectively.


Psychotic : $\bar{x}_1 = 0.032$ and $S_1 = 0.003$
Not Psychotic : $\bar{x}_2 = 0.014$ and $S_2 = 0.002$

At 1% significance level does the data suggest dopamine levels are higher among patients who have psychosis?

My attempt:

H_o= $\mu_1 - \mu_2 = 0$
H_a= $\mu_1 - \mu_2 > 0$

We can assume the H_o to be true and therefore $= 0$


$\bar{x}_1 - \bar{x}_2 = 0.018$

I'm going to assume that the data follows a t-distribution because n = 11 for each data set. We need to find the t-value at which the probability of being above is 1% at 22 degrees freedom (degrees freedom = n₁ +n₂ = 22). From the tables t_0.01,22 = 2.508

Next we need to work out $\sigma$ and see if 0.018 is further from $\mu$ than $2.508 \sigma$.

$\sigma = \sqrt{((0.003)^2/11+(0.002)^2/11)} = 0.001087$


$2.508 \sigma = 0.00273$. 0.018 is much larger than that number and so lies far to the right of the critical value. This means that we can reject our null hypothesis and conclude that dopamine levels are higher in patients that have psychosis.

I feel like I've gone wrong somewhere because 0.018 is so much larger than the critical value of 0.00273. If anyone could look over this and confirm weather I'm right or not it would help lots! Thanks in advance.