A county contains several municipalities.
Ammerland is more than a name on a landscape map. This question concerns an administrative unit with a county council and county administration. Westerstede is the town where that administration is based; the county also includes the other five municipalities listed.
An address in Bad Zwischenahn or Rastede therefore does not indicate a different federal state. Both belong to this county. Concrete place names help distinguish a municipality from the county level.

The other three answers
The other three names are real counties, but in other states.
Rhein-Sieg-Kreis
Rhein-Sieg-Kreis is in North Rhine-Westphalia, around Bonn. It does not belong to Niedersachsen.
Nordfriesland
Nordfriesland is in Schleswig-Holstein. Being on the North Sea does not automatically make a county part of Niedersachsen.
Vogtlandkreis
Vogtlandkreis is in Saxony. It must not be confused with Ammerland in north-western Germany.
County town and state capital belong to different levels.
Westerstede is Ammerland’s county town; Hannover is Niedersachsen’s capital. The county administration replaces neither the individual municipal administrations nor the state government.
Correct territorial classification is enough for this question. Landscape regions, tourism areas and electoral districts may have different boundaries from a county. The official county designation is therefore the more reliable clue.
Westerstede and five municipalities · Ammerland county ↗Ammerland → Niedersachsen; county town → Westerstede.
Bad Zwischenahn is one example of a municipality in the county.
Three words for this question
- der Landkreiscounty
- A local territorial unit containing several municipalities.
- die Kreisstadtcounty town
- The seat of the county administration.
- die Gemeindemunicipality
- A local administrative unit, which may or may not belong to a county.
