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 \(\displaystyle{S}.{E}.{\left(\overline{{x}}\right)}={0.4}\)