Learn Russian: У скольких респондентов вы взяли интервью для этого опроса? - How many respondents did you interview for this survey?

In Russian, you cannot "interview someone" directly. The standard phrasing is взять интервью у кого-то (literally "to take an interview from someone"). The preposition у requires the Genitive case, so the quantifier сколько must change to its Genitive form, скольких.

Is респондентов in the Genitive case just because сколько is a quantity word?

Not exactly! In the Nominative or Accusative cases, сколько forces the following noun into the Genitive. However, when сколько is put into an oblique case (like the Genitive скольких here, required by у), it acts like an adjective and agrees with the noun's case. So both скольких and респондентов are Genitive plural, matching each other.

Why doesn't the word интервью have a case ending?

Интервью is a borrowed foreign word. In Russian, most borrowed nouns that end in a vowel (like кафе, метро, and интервью) are indeclinable, meaning their spelling never changes. Here it is technically in the Accusative case as the direct object of взяли, but it looks exactly the same as in the dictionary.

Why does the sentence end with этого опроса?