One hundred ninety-one of the 288 high school students surveyed at a local school say they went outside more during school hours as elementary school students than they do now as high school students. Calculate the margin of error (ME), rounded to the nearest tenth of a percent. Is it reasonable that the state education department claims the percentage for the entire state is 73%? Justify your answer.
A:Yes, it is reasonable because the ME is 2.8% and the population proportion of 73% falls within the sample interval of 66.3% ± 2.8%
B:No, it is not reasonable because the ME is 5.6% and the population proportion of 73% falls outside the sample interval of 66.3% ± 5.6%
C:Yes, it is reasonable because the ME is 5.6% and the population proportion of 66% falls within the sample interval of 73.0% ± 5.9%
D:No, it is not reasonable because the ME is 4.3% and the population proportion of 73% falls outside
