Interpreting a paired t-test for price means

Hey everyone,

I am new to this, but I would be extremly thankful, if someone could help me with this.

I research the topic of rate parity for hotels in Germany, which involves comparing rate means for different distribution channels.
I have performed a paired t-test for the "phone rate mean" and the "website rate mean" with the help of a website.

Until I read again in my business research methods book, I was fairly certain how to interpret the results, but now I am confused..
So here are the numbers:

Phone Mean: 223.21
Standard Deviation: 102.36

Website Mean: 208.67
Standard Deviation: 106.09

Degrees of freedom: 167
alpha: .05

The results, which the program showed me:
t-value 3.7489
p-value 2-tailed 0.0002

What I thought how I would have to interpret this is, that I reject my H0, because when comparing the p-value to my alpha, it is smaller.
Is this the right conclusion? Especially, I want to know, if comparing the alpha to the p-value is right, because I have read, that you have to calculate r (or something like that) and then compare it to a table.

I hope someone can help me with this; I would be very very thankful!

Best wishes,