Question

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 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 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 "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 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.) .039 (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.) X % to 20 X % 10

Answer 1

Sal! Given, n = 695 Ô = 0.38 (a) option (E) is correct. Margin of error is - interval At 95% confidence 2-0.05, 2012 = 1.96 M.E Za12* Ô (1-Å n 1.96* 0:38 (1-0.38) 0-03608 6 g 5 E = 0 36 (6) 957 confidence interval is. C I - P t 0.38 + 0.036 = 0.416) o (0.344 ( 34.4.1. 41.6.7.) ) 95%. CI 34.41% to 41.614