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Chapter 8: Q9E (page 325)

Water samples are taken from water used for cooling as it is being discharged from a power plant into a river. It has been determined that as long as the mean temperature of the discharged water is at most 150掳F, there will be no negative effects on the river鈥檚 ecosystem. To investigate whether the plant is in compliance with regulations that prohibit a mean discharge water temperature above 150掳, 50 water samples will be taken at randomly selected times and the temperature of each sample recorded. The resulting data will be used to test the hypotheses H0: 碌= 1500 versus Ha: 碌> 1500. In the context of this situation, describe type I and type II errors. Which type of error would you

consider more serious? Explain.

Short Answer

Expert verified

It is difficult to decide which error is more serious. Perhaps the type II error is more serious because it would affect the ecosystem more.

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 type I error is to conclude that the plant is not in compliance when it is bigger that \(150\)when it is \(150\).

The type II error is to conclude that the plant is in compliance when in fact it is not.

It is difficult to decide which error is more serious. Perhaps the type II error is more serious because it would affect the ecosystem more. Depending on what you think is more serious you can adjust the hypotheses

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