Although television brings the world into their homes, students in American public schools have very serious gaps in their knowledge about other countries, according to a nationwide survey sponsored by the U.S. Office of Education.

About four out of 10 high school seniors who took part in the survey thought Israel was an Arab nation. Some 27 per cent of them thought Golda Meir, the former Israeli prime minister, was president of Egypt.

Only slightly more than half the seniors - 59 per cent - could locate Egypt on a map about 16 per cent placed Egypt where India is, 5,000 miles away.

The survey, which cost $175,000, was conducted by Educational Testing Service in the fall of 1974. It involved about 1,800 students in the fourth, eighth, and 12th grades picked at random in a cross-section of schools in 27 states.

Overall, the study reported, students say that television has the most impact on their attitudes about the world. But in geographic regions given a great deal of attention on television but relatively little in schools such as the Middle East, the study said many students make serious factual errors, and the percentage making mistakes does not decline much from grade to grade.

On the other hand, the study showed, for countries that are emphasized in social studies instruction, such as England and Russia there are substantial gains in information as students move through school.

Still, the mistakes that even 12th graders make about basic political and geographical facts are substantial.

For example, when asked which of four countries - China, India, Poland, or Russia - is located in both Europe and Asia, only 54 per cent said Russia, the right answer.

When asked to pick a country where the same political party has been in power since 1939, 30 per cent said West Germany, despite World War II. About 30 per cent correctly picked Mexico, but 26 per cent said Great Britain and 12 per cent said the United States.

On another multiple choice question: For what purpose has the U.S. government spent the most money since World War II? Only 46 per cent picked defense, the correct answer. Some 41 per cent said space travel, 8 per cent said education, and 6 per cent said transportation.