Are the Lapita the ancestors of the Polynesians and the Maori?

Probably, although this connection hasn't been definitely proven.

http://en.wikipedia.org/wiki/Lapita

Yes, the Lapita are believed to be the ancestors of the Polynesians and the Maori.

To determine if the Lapita are indeed the ancestors of the Polynesians and the Maori, we can look at archaeological evidence and linguistic similarities.

1. Archaeological evidence: The Lapita culture was an ancient Pacific Oceanic culture that existed between 1600 BCE and 500 BCE. Lapita pottery has been found in numerous locations across the Pacific, including areas where the Polynesians and the Maori eventually settled. This suggests a potential connection between the Lapita and these later cultures.

2. Linguistic similarities: Linguistic analysis supports the connection between the Lapita, Polynesians, and Maori. The languages of these cultures share similarities in vocabulary, phonetics, and grammar, which indicates a common ancestry.

3. Genetic studies: Genetic research also lends support to the idea that the Lapita are the ancestors of the Polynesians and the Maori. Studies have revealed genetic links and patterns between modern-day Polynesians, including Maori populations, and ancient Lapita people.

By examining these archaeological, linguistic, and genetic sources, researchers have established a connection between the Lapita and the Polynesians and Maori. They can be considered ancestral to these groups, although it's important to note that cultural and genetic blending likely occurred with other populations throughout history.