A research organization claims that the monthly wages of industrial workers in district X exceed those in district Y by more than Rs 150. Two different samples drawn independently from the two districts yielded the following results:
>District X: x1 bar = 648,
s1^2 = 120, and
n1 = 100
>District Y:
x2bar = 495,
s2^2 = 140, and n2 = 90
Verify at a 0.05 level of significance whether the sample results support the claim of the organization.
For this solutions I used the formula $$Z = \frac{\bar x_1- \bar x_2}{\sqrt{s_1^2/n_1+s_2^2/n_2}}$$ which gives me the answer $92.7$. Is this the correct Z-score how to verify it for a $0.05$ level of significance (new to this area)?
Can anyone tell me can I conclude since the result is 92.7 the results support the claim made by the research organization ?