Can we use t-test to liner combination of random variables?

17 Views Asked by At

Suppose X and Y are two random variables.

And I have some samples of them:

[9, 10, 11, 9, 10, 8, 10] and [100, 99, 101, 110, 120].

I want to test if Y is statistically larger than 10*X,

Question:

Can I use t-test and assume H0: 10*X ≤ Y with alpha=0.05?

I am asking because I have never seen any case that applies 10* before a random variable. All examples tell me I can use H0: X ≤ Y instead of 10*X ≤ Y

Thanks.