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A regular type of laminate is currently being used by a manufacturer of circuit boards. A special laminate has been developed to reduce warpage. The regular laminate will be used on one sample of specimens and the special

laminate on another sample, and the amount of warpage will then be determined for each specimen. The manufacturer will then switch to the special laminate only if it can be demonstrated that the true average amount of warpage for that laminate is less than for the regular laminate. State the relevant hypotheses, and describe the type I and type II errors in the context of this situation.

Short Answer

Expert verified

The relevant hypotheses are \({H_0}:{\mu _1} = {\mu _2}\)versus \({H_a}:{\mu _1} > {\mu _2}\).

Step by step solution

01

Errors in Hypothesis testing.

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.

02

Step 2:Test statistic.

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.

03

Hypothesis results.

Before stating the relevant hypotheses, denote with \({\mu _1}\) the average for the regular laminate, and with \({\mu _2}\) the average for the special laminate.

The relevant hypotheses are \({H_0}:{\mu _1} = {\mu _2}\)versus \({H_a}:{\mu _1} > {\mu _2}\).

The type I error is to conclude that the war page for special laminate is less than the regular laminate when it is not.

The type II error is to conclude that there is no difference in the laminates when the special laminate produces less war page.

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