Question

# Express the confidence interval 172.3<\mu<229.1 in the form of \bar{x}\pm ME.

College Statistics

Express the confidence interval $$\displaystyle{172.3}{<}\mu{<}{229.1}$$ in the form of $$\displaystyle\overline{{{x}}}\pm{M}{E}.$$

2021-08-08

Step 1
We know that,
$$\displaystyle\overline{{{X}}}-{M}.{E}.{<}\mu{<}\overline{{{X}}}+{M}.{E}.$$
(1) $$\displaystyle\overline{{{X}}}-{M}.{E}.={172.3}$$
(2) $$\displaystyle\overline{{{X}}}+{M}.{E}.={229.1}$$
By adding (1) and (2), we have
$$\displaystyle{2}\overline{{{X}}}={172.3}+{229.1}$$
$$\displaystyle\overline{{{X}}}={\frac{{{401.4}}}{{{2}}}}$$
$$\displaystyle\overline{{{X}}}={200.7}$$
and,
$$\displaystyle{M}.{E}.={200.7}-{172.3}$$
$$\displaystyle{M}.{E}.={28.4}$$
Answer $$\displaystyle={ \bar{X}\pm M.E.=200.7\pm28.4 }\$$