One hundred forty-one of the 224 high school students surveyed at a local school say they plan on taking some form of postsecondary education. 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 68%? Justify your answer.
A: Yes, it is reasonable because the ME is 5.6% and the population proportion of 68% falls within the sample interval of 62.9% ± 5.6%
B: No, it is not reasonable because the ME is 3.2% and the population proportion of 68% falls outside the sample interval of 62.9% ± 3.2%
C: Yes, it is reasonable because the ME is 6.5% and the population proportion of 68% falls within the sample interval of 62.9% ± 6.5%
D: No, it is not reasonable because the ME is 6.5% and the population proportion of 63% falls outside the sample interval of 68.0% ± 6.5%
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