A simple random sample of students at a certain college were surveyed and asked whether they were satisfied with college life. Two hundred eighty of them replied that they were satisfied. The Dean of Students claims that more than half of the students at the college are satisfied. To test this claim, a test of the hypotheses versus is performed. The -value is . The -value is very small, so is rejected. Whose interpretation of the -value is correct? The alumni director says because is very small, the population proportion must be much greater than . The head of admissions says that because the -value is very small, we can be fairly certain that the population proportion is greater than , but we cannot be certain that it is a lot greater