Question: Are Howea belmoreana and Crinodendron in the same family?

Context paragraphs:
Howea: Howea is a genus of two palms, "H. belmoreana" and "H. forsteriana", both endemic to Lord Howe Island, Australia.  "H. forsteriana" in particular is commonly grown as an indoor plant in the Northern Hemisphere, and the two species form the mainstay of the island's palm seed industry and more importantly its trade in newly germinated seedlings.  The palms are also cultivated on Norfolk Island, where seeds are produced for export.

Howea forsteriana: Howea forsteriana (Kentia Palm or Thatch palm) is a species of flowering plant in the palm family Arecaeae, endemic to Lord Howe Island in Australia.  It is also widely grown on Norfolk Island.  It is a relatively slow-growing palm, eventually growing up to 10 m tall by 6 m wide.  Its fronds can reach 3 m long.

Crinodendron: Crinodendron is a botanic genus with 8 species of flowering plants belonging to the family Elaeocarpaceae.  They are evergreen shrubs or small trees native to the forests of Chile.  They have narrow, leathery evergreen leaves and pendent bell-shaped flowers in red, pink or white.

Howea belmoreana: Howea belmoreana, the curly palm, kentia palm, or Belmore sentry palm, is a species of flowering plant in the family Arecaceae, endemic to Lord Howe Island, Australia.  It and "Howea forsteriana" probably evolved from a common ancestor through sympatric speciation.  The canopy of a mature kentia palm tree spreads 5 - in diameter and contains roughly 36 leaves.

Crinodendron hookerianum: Crinodendron hookerianum, known as the Chilean lantern tree, is an evergreen tree in the family Elaeocarpaceae.  It is endemic to Chile, where it occurs from Cautin to Palena (38 to 43°S).  It grows near streams and in very humid and shady places.

Supporting paragraphs: Howea belmoreana Crinodendron
Answer: no