A private study indicates as many as 5 million children are going to bed hungry in the United States.

The Food Research and Action Center made what it called the conservative estimate after a house-to-house survey of nearly 800 low-income families in Washington state and said it would extend the study to seven other states over the next 15 months.But on the basis of the early data from Washington state "We estimate conservatively that 2 million to 5 million children in this country could now have a serious hunger problem," Robert J. Fersh, executive director of the center, said Monday.