Hello Nitin,
As Jorg said, you definitely need more than just the average of two periods.
I think you have 10 timesteps since you want to know whether the difference of the JJAS means between the two periods are significant or not (June, July, August and September in the same year would not be independent).
You can see here an example using Welch-test how to do significance test for two 30-years of temperature means.
let var1=xi[l=1:30@var]
let var2=yi[l=1:30@var]
let ave1=xi[l=1:30@ave]
let ave2=yi[l=1:30@ave]
let diffave=ave2-ave1 !difference
let frec=(1/29)*(((var1/30)/(var1/30+var2/30))^2)+(1/29)*(((var2/30)/(var1/30+var2/30))^2)
let f1=int(1/frec) !degrees of freedom
!here is the "built-in" t-table to determine whether it is significant or not at 95% level