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Given that, the average number of occupational accidents is less than 70.

Here we use a one-tailed test.

Therefore, the null and alternative hypotheses are given by

\(\begin{aligned}{H_0}:\mu = 70\\{H_a}:\mu < 70\end{aligned}\)

For,

\(\begin{aligned}\alpha & = 0.01\,\\and\,\\df &= n - 1\\ &= 2\end{aligned}\)

The one-tailed rejection region is \(t < - {t_{0.01}} = - 6.965\).

Given that, \(\bar x = 64\,,\,s = 35.3\)

The test statistic is computed as

\(\begin{aligned}t &= \frac{{\bar x - \mu }}{{\frac{s}{{\sqrt n }}}}\\ &= \frac{{64 - 70}}{{\frac{{35.3}}{{\sqrt 3 }}}}\\ &= \frac{{ - 6}}{{20.38}}\\ &= - 0.2944\end{aligned}\)

Therefore, the test statistic is -0.2944.

We observed that the calculated test statistic is greater than the tabulated test statistic. The calculated t falls outside of the rejection region; the inspector cannot reject the null hypothesis.

There is insufficient evidence to conclude that \(\mu < 70\) . Here the sample size is three. The sample is taken from an average population is satisfied for the test result to be valid.