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Chapter 8: Q5E (page 325)

To determine whether the pipe welds in a nuclear power plant meet specifications, a random sample of welds is selected, and tests are conducted on each weld in the sample. Weld strength is measured as the force required to break the weld. Suppose the specifications state that mean strength of welds should exceed 100 lb/in2 ; the inspection team decides to test H0: 碌= 100 versus Ha: 碌> 100. Explain why it might be preferable to use

this Ha rather than 碌 < 100

Short Answer

Expert verified

The non-compatibility is better in this case because we are interested in the force required to break the weld, the non-compatible claim.

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.

The statement of hypothesis \({H_0}\) is that the weld strength does not meet specifications. The hypothesis is reject when there is strong evidence that it should be rejected, evidence to the contrary.

The hypothesis \({H_a}:\mu < 100\) would yield results that the weld strength is compatible with the specifications unless proved otherwise. However, the non-compatibility is better in this case because we are interested in the force required to break the weld, the non-compatible claim

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