It was in "One Night in the Tropics" (on the Best of Abbott and Costello Vol. 1) but that was only a shortened version. The longer and widely considered the best version appears on "The Naughty Nineties" (on Vol. 2). If you listen closely, you can hear the production crew laughing.
You can buy these dvds for pretty cheap. 8 movies on each collection and only for $20 but I'm sure you can find them on sale.
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Marlowe21