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The Economist magazine reports from a study of 300 subscribers that the average income is \(\$ 80,000\) USD with a standard deviation of \(\$ 15,000\) USD.

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The Economist magazine reports from a study of 300 subscribers that the average income is \(\$ 80,000\) USD with a standard deviation of \(\$ 15,000\) USD. How close to that would the real average income of all subscribers be with \(95 \%\) confidence?
in Data Science & Statistics by Platinum (102k points) | 266 views

1 Answer

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\[
\begin{gathered}
P\left(\bar{x}-1.96\left(\frac{15000}{\sqrt{300}}\right) \leq \mu \leq \bar{x}+1.96\left(\frac{15000}{\sqrt{300}}\right)\right) \\
=+/-\$ 1697.41
\end{gathered}
\]
So, with \(95 \%\) confidence, the actual average income range for all subscribers would be between \(\$ 81,697\) and \(\$ 78,302\).
by Platinum (102k points)

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