Ramsey

## Answered question

2021-08-23

Suppose that you are testing the hypotheses

A sample of size 16 results in a sample mean of 11.5 and a sample standard deviation of 1.6.
What is the standard error of the mean?

### Answer & Explanation

Viktor Wiley

Skilled2021-08-24Added 84 answers

The hypotheses is given by Null Hypothesis ${H}_{0}:\mu =11$.
Alternating Hypothesis ${H}_{A}:\mu >11$
The sample size $n=16$, the sample mean $\stackrel{―}{x}=11.5$ and sample standard deviation s=1.6.
By the standard error of the mean we note the following: Let the sample size be n, sample mean mean barx, and sample standard deviation is s then the formula for standard error of the mean is
$S.E.\left(\stackrel{―}{x}\right)=\frac{s}{\sqrt{n}}$
Using the above formula we have the standard error of the mean is
$S.E.\left(\stackrel{―}{x}\right)=\frac{s}{\sqrt{n}}=\frac{1.6}{\sqrt{16}}=\frac{1.6}{4}=0.4$
Therefore, the standard error of the mean is $S.E.\left(\stackrel{―}{x}\right)=0.4$

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