Translation:The rich American man is in the study.
Just to clarify: your dictionary is not wrong. Dolgozó means both "working" and "working person = worker". Hungarian makes little difference between adjectives (and participles) and the respective nouns. So you have magas meaning tall, and "egy magas" can refer to a tall person (or object), where you would say in English "a tall one". Likewise, "a nevető" can simply mean "the laughing person".
Szoba is not a suffix, it's an own noun, simply meaning "room". Words like dolgozószoba are compound nouns. Just two nouns smooshed together, like the English "teacup" (teáscsésze, by the way. Bit of a tonguetwister. Which is also a compound noun.) So you can translate dolgozószoba as "working room", neat and simple.
Dolgozó means "working", as we already found out. Then you have fürdőszoba - bathroom. Fürdő simply means "bathing", from the verb fürdik - to bathe. Hálószoba - bedroom is a bit of a special case. The translations you can find for háló tell you it's "net" or "web", but it is also a (more archaic) word for "sleeping".
I think these three are the only ones discussed in this course that have szoba in their name. You can also have things like gyerekszoba - children's room, or várószoba - waiting room.
The living room - nappali, is also sometimes just referred to as szoba. "Gyerünk a szobába." - "Let's go to the (living) room."
Thank you for this nice explanation, which I would like to expand a bit. Most important, "nappali" is not synonymous to "szoba". In fact, children's room or bedroom can be also referred to as "szoba". "Dolgozószoba" is not a compound of two nouns, but of a present participle (called "folyamatos melléknévi igenév" in Hungarian) and of a noun. "Hálószoba" has nothing to do with "háló" as "net" or "web". Its "háló" part is also a present participle, derived from the verb "hál", which means (if used with locative) "to sleep somewhere overnight" or (if used together with a nominal that has the suffix -val/-vel) "to have sex (with somebody)".
Ksenia, in German there's "Arbeitszimmer" for that. :)
Hungarian's efficiency lies elsewhere. It's an agglutinative language, and it's typical for those languages to have a rather small number of morphemes. Morphemes are the smallest meaningful word units, like "small", "-est", "mean", "-ing", "-ful", "word", "unit" and "-s". Rather than creating, choosing or adopting new morphemes, agglutinative languages rather use the morphemes they have to build up the desired meaning:
- compute + -er = szám + -ít + -ó + gép ("number" + "-ate" + "-ing" + "machine")
- police = rend + őr + -ség ("order" + "keeper" + "-ship")
- dent- + -ist = fog + orvos ("tooth" + "doctor")
- watch = kar + óra ("arm" + "clock")
So while English juggles with morphemes like "work", "job", "study", "employ" and similar, Hungarian is good with just using "dolgoz-" and modifying it into the desired direction. You want to talk about a room that you use for working? Why not call it "work-ing room", "dolgoz-ó-szoba"?
In more technical terms, English is memory-heavy, because you have to learn a lot of words that look different even if they have a related meaning, like "tooth", "dental", "fang" or "molar". Hungarian is computation-heavy, since you have fewer different morphemes to learn (all the toothy things can be expressed with combinations of fog), but you have to remember to combine them in the right way to get the correct meaning across.