# Suppose that you are testing the hypotheses\displaystyle{H}_{{0}}:\mu={11}{v}{s}{H}_{{A}}:\mu>{11}. 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?

Suppose that you are testing the hypotheses
$$\displaystyle{H}_{{0}}:\mu={11}\ {v}{s}\ {H}_{{A}}:\mu>{11}.$$
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?

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Viktor Wiley

The hypotheses is given by Null Hypothesis $$\displaystyle{H}_{{0}}:\mu={11}$$.
Alternating Hypothesis $$\displaystyle{H}_{{A}}:\mu>{11}$$
The sample size $$n=16$$, the sample mean $$\displaystyle\overline{{x}}={11.5}$$ 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
$$\displaystyle{S}.{E}.{\left(\overline{{x}}\right)}={\frac{{{s}}}{{\sqrt{{n}}}}}$$
Using the above formula we have the standard error of the mean is
$$\displaystyle{S}.{E}.{\left(\overline{{x}}\right)}={\frac{{{s}}}{{\sqrt{{n}}}}}={\frac{{{1.6}}}{{\sqrt{{16}}}}}=\frac{1.6}{{4}}={0.4}$$
Therefore, the standard error of the mean is $$\displaystyle{S}.{E}.{\left(\overline{{x}}\right)}={0.4}$$