ASK YOUR TEACHER PRACTICE ANOTHER Suppose a poll conducted at a certain college during their most recent spring semester asked 675 college students whether or not a privately owned dining hall should be allowed on campus. The response "Yes, it should" was selected by 30% 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 a 4 percentage points." Explain what the statement means. It means that the researchers are 87% confident that the proportion answer "Yes, it should represents the proportion of all students at this college. It means that the proportion answering "No, it shouldn't" in the proportion of all students at this college is within 4% of the proportion answering "Yes, it should." It means that the researchers are 91% confident that the proportion answer "Yes, it should" represents the proportion of all students at this college It means that the proportion answering "Yes, it should" in the sample is probably within 8% of the proportion of all students at this college It means that the proportion answering "Yes, it should" in the sample is probably within 4% of the proportion of all students at this college 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.) (b) 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.) % to (c) Suppose a similar poll was conducted during the previous fall semester found that 17% of the respondents said "Yes, it should." Do you think the difference between the results of the two polis can be attributed to chance variation in the samples taken, or does it represent a real difference of opinion in the college population in the spring semester versus the fall semester? Explain (Round your answers to one decimal place, when necessary.) It probably represents a real difference of opinion % to %, which does not overlap If the margin of error for each poll is at most 4%, then a confidence interval for the fall semester poll should be no greater than with the confidence interval given in part (b) for the spring semester poll Need Help? Wh