Question

153 of the 258 high school students surveyed at a local school said they went outside more during school hours as elementary school students than they do now as high school students. calculate the margin of error, rounded to the nearest tenth of a percent. is it reasonable that the state education department claims the percentage for the entire state is 63%? jusify your answer.

Answer 1

Answer-

It is reasonable that the state education department claims the percentage for the entire state is 63%.

Solution-

153 out of the 258 high school students surveyed at a local school said they went outside more during school hours as elementary school students than they do now as high school students.

Here,

x = 153,

n = 258,

Then,

$\text{sample proportion}=p=\dfrac{153}{258}=0.5930=59.30\%$

And,

$\text{Margin Error}=2\times \sqrt{\dfrac{p(1-p)}{n}}$

Putting the values,

$\text{ME}=2\times \sqrt{\dfrac{(0.5930)(1-0.5930)}{258}}\\\\=2\times \sqrt{\dfrac{(0.5930)(0.407)}{258}}\\\\=2\times \sqrt{\dfrac{0.2414}{208}}\\\\=2\times 0.0341\\\\=0.0682\\\\=6.82\%$

The interval would be,

$=(59.30-6.82,\ 59.30+6.82)\\\\=(52.48,\ 66.12)$

As population proportion p=63% lies in this interval, so it is reasonable.