level of significance

#1
A researcher claims the mean IQ of students in the Faculty of Medicine exceeds that of students in other faculties. It is known that the mean IQ of students in other faculties is 120. A random sample of 36 medical students showed a mean IQ of 125 and a standard deviation of 10. do the sample statistics prove the researcher’s claim is true to a 0.01 level of significance.

Pls tell me if im correct with my answer.

Ho:U=120
Ha:U>120

Df=n-1=36-1=35
tn-1;a=T35;0.01=2.438

We will reject the null hypothesis if the test statistic is greater than 2.438

N=36
X=124
S=10

Tcal=125-120 /{10/ 36(square root)}= 5/1.666=2.999

Since the test statistic is greater than the critical value we reject the null hypothesis.