The Reagan administration yesterday replied to study showing that 20 to 25 million people, most of them living below the poverty line, would be hurt by its economic program by saying the study has been misinterpreted and really shows that the "truly needy" would not be hurt by the plan.

Office of Management and Budget Director David A. Stockman said the study, by the Congressional Budget Office, is welcome because it shows that 96 percent of low-income families would not suffer any significant loss of spendale income.

Stockman said, "If you want to analyze [the study] fairly and objectively," what should be stressed is that of the 16.5 million people living with an annual income of less than 150 percent of the poverty-line income of $8,410 for a family of four, 15 percent would gain under the Reagan program, 34 percent would have no change in spendable income and 47 percent would suffer a loss of between 1 and 5 percent of their spendable income.

He was asked whether a cut of 5 percent would not be painful for a family living at the poverty level.

"I don't think so," Stockman replied.

The architect of the federal spending cut program added that tha CBO study does not take into account what for administration officials has become in an important article of faith: that the president's economic program of spending and tax cuts, if approved, would lower inflation, bring down interest rates and stimulate growth and employment so that its benefits to the poor would "vastly outweigh" its cuts.

On the other hand, Stockman did not take into account the CBO's statement that its figures "considerably understate" the real impact of the budget cuts because it measured only about a third of them.

The impact of $5.3 billion in fiscal 1982 cuts in welfare, public service job and food programs was measured, but the effect of $10.1 billion in cuts, including Social Security, Medicaid and unemployment insurance, could not be calculated because of a lack of data, the CBO said.

Stockman made an unannounced appearance in the White House press room to give the administration's interpretation of the CBO numbers.

On another subject, he said he expect that the Senate Budget Committee will give its approval quickly to the Reagan budget plans when the Senate returns from the Easter recess.

"It was only an accounting argument in the first place, and it can be solved by an accounting solution," Stockman said of the vote last week, when three Republicans joined Budget Committee Demcorats to deal the Reagan plan an unexpected defeat.

At the time of the vote, the defecting Republicans complained that the Reagan administration refused to tell them what further budget cuts it planned for fiscal 1983 and 1984 to balance the budget.

Stockman denied to reporters that he planned to outline those future cuts to win votes when the committee takes up the budget blueprint a second time.

In another development, the White House released a study revealing what President Reagan called "startling statistics" on government waste and fraud.

The study by the Merit Systems Protection Board and the Inspectors General found that 45 percent of the more than 8,000 federal employes who responded said they had first-hand knowledge of waste, fraud or mismanagement in their agencies.

However, 43 percent of those who reported such abuses said nothing was done, and large numbers of cases went unreported because the federal employes thought that no action would result.

"I want it made clear that today," the president said, his administration assures protection and proper investigation of allegations "to every whistleblower in the federal government."

Reagan's statement, released by his press office, said that the study confirms his conviction that large amounts of money can be saved simply by eliminating fraud and waste.