Step 1

Determine the t-value by looking in the row starting with degrees of freedom \(\displaystyle{n}-{1}={7}-{1}={6}\) in table \(\displaystyle{a}-{3}\):

\(\displaystyle{t}_{{\frac{\alpha}{{2}}}}={t}_{{{0.01}}}={3.143}\)

The margin of error is then:

\(\displaystyle{E}={t}_{{\frac{\alpha}{{2}}}}\cdot{\frac{{{s}}}{{\sqrt{{{n}}}}}}={3.143}\cdot{\frac{{{0.0389}}}{{\sqrt{{{7}}}}}}\approx{0.0462}\)

The confidence interval is:

\(\displaystyle{0.0752}={0.1214}-{0.0462}=\overline{{{x}}}-{E}{<}\mu{<}\overline{{{x}}}+{E}={0.1214}+{0.0462}={0.1676}\)

Step 2

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