Is there stars in the sky when there is no moon that you can see?

Answer:

Yes indeed. In fact, the moon light obliterates starlight from the dimmer suns. Amateur astronomers prefer to pick "star parties" every other fortnight when the moon is new (opposite of "full") for that reason.

In fact, there are also stars in the day, it is just that their light is obliterated by the very bright sun. Although Saturn is a planet, not a star, you can see Saturn in a telescope long after the sun rises. If you know right where to look, you can also see Venus, another planet.

When the moon blocks out the sun, as during a total eclipse, the daylight stars shine forth. You see these same stars six months later, when the earth and moon are on the opposite side of the sun.