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%