One hundred twelve of the 158 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 80%? Justify your answer. (7 points) Hint: ME equals plus or minus two times square root of start fraction p hat left parenthesis one minus p hat right parenthesis over N end fraction end square root , where p hat is the yes proportion in the sample and N is the sample size

Yes, it is reasonable because the ME is 7.2% and the population proportion of 71% falls within the sample interval of 80.0% ± 7.2%
No, it is not reasonable because the ME is 3.6% and the population proportion of 80% falls outside the sample interval of 70.9% ± 3.6%
Yes, it is reasonable because the ME is 6.2% and the population proportion of 80% falls within the sample interval of 70.9% ± 6.2%
No, it is not reasonable because the ME is 7.2% and the population proportion of 80% falls outside the sample interval of 70.9% ± 7.2%