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A type I error consists of rejecting the null hypothesis H₀ when it is true.

A type II error involves not rejecting H₀ when it is false.

A test statistic is a function of the sample data used as a basis for deciding whether H₀ should be rejected. The selected test statistic should discriminate effectively between the two hypotheses. That is, values of the statistic that tend to result when H₀ is true should be quite different from those typically observed when H₀ is not true

The hypotheses are \({H_0}:\sigma = 0.05\) versus \({H_a}:\sigma < 0.05\), where \(\sigma \) is the population standard deviation. Polyethylene sheaths will be used unless hypothesis \({H_0}\) is rejected, therefore the burden on proof is on the data to show that the true standard deviation of sheath thickness is not less than \(0.05\)- the sheaths will be used unless \({H_a}\) is accepted.

The type I error is to conclude that \(\sigma \)is less that \(0.05\) when it is equal to \(0.05\).

The type II error is to conclude that \(\sigma \)is \(0.05\) when it is \(0.05\).