Suppose a poll conducted at a certain college during their most recent spring semester asked 695 college students whether or not a privately owned dining hall should be allowed on campus. The response "Yes, it should" was selected by 38% of the respondents.

(a) Suppose the researchers who conducted the poll reported "For results based on the total college population, once can say with 95% confidence that the margin of sampling error is no greater than ± 4 percentage points." Explain what the statement means.

Verify this statement by finding the conservative margin of error for a 95% confidence interval for this sample. (Round your answer to three decimal places.)

Using the conservative margin of error found in part (a), give a 95% confidence interval for the percentage of all college student at this school who said the dining hall should be allow. (Round your answers to one decimal place.)