Question

One hundred sixty-five of the 225 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 78%? Justify your answer.

Answer 1

It is reasonable because the ME is 5.9% and the population proportion of 78% falls in the  sample interval of 73.3% ± 5.9%  

or 

Yes, it is reasonable because the ME is 5.9% and the population proportion of 73% falls within the sample interval of 78.0% ± 5.9% 

either one will work