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Scenario

I have the avg room price for all the hotels of my chain (32 observations of the 32 hotels). Then I have the avg room price for a sample of competitors (60 observations taken from a larger population).

Problem

I would like to understand whether the avg room price of the hotels of my chain is equal to that of the competitors

Proposed solution

First, I computed the average room price across all the hotels of my chain $p_a$. Since the entire population is known, I would say that there is no uncertainty here, this is the exact average.

Then I computed the average room price of the sample of competitors and the related std deviation ($barp_c$ and $tildesigma_c$).

I performed a hypothesis testing with the null $H_0: p_c = p_a$ against the alternative $H_1: p_c neq p_a$. The test statistic is then ($n=60$):
$$
t = fracbarp_c-p_afractildesigma_csqrtn
$$
If the associated p-value is sufficently low, I reject the null hypothesis.

Basically here I'm considering that the average room price of the hotels of my chain is known and well-established, hence I'm doing the hypothesis testing for a single population mean (the competitors' population). Do you think this is the right approach or shall I test a hypothesis about two population mean (this is the alternative that comes to my mind)

Thanks for any help, T.

This seems completely reasonable to me. It is what I would have done.

It depends on what you're really trying to do.

One thing that immediately comes to mind is that hotel prices depend heavily on location. So the price of a hotel room in NYC is apt to be much higher than the price of a hotel in Bismark, ND.

So a better statistic might be to do a paired T test, where the price for each of your hotels is compared to a comparable hotel in the same market place.