Question

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

College Statistics
ANSWERED
asked 2021-08-02

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

Answers (1)

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 \(\displaystyle={ \bar{X}\pm M.E.=200.7\pm28.4 }\ \)

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