# Statistics - Alpha and Beta Risk - Risk Management

How might type I and type II errors relate to quality control and risk management in differing industries?For example, manufacturing pharmaceuticals versus shoes? Which industries might opt toward one error over another and why?

Description on the following:

Type I error -- Wrongful Rejection (Alpha risk)

Type II error -- Wrongful acceptance (Beta risk)

How would hypothesis testing work in a service industry?

The detailed answer is given in the attached answer file.

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#### Solution Preview

Type I error -- Wrongful Rejection (Alpha risk)

Answer:

A hypothesis test concludes with a decision : H0 is accepted or H0 is rejected.

A type I error occurs when H0 is rejected while it is in fact true.

A P-value can be thought of as a descriptive statistic that measures how much support the data give to the null hypothesis: the smaller the P-value, the less the support, and therefore, we reject the null hypothesis. But what level of support is considered so small that the null hypothesis should be rejected? Statisticians answer this question by considering the risk of error involved in the decision, specifically the risk of type I error, rejecting H0 when it is true. They know that for a given sample, the smaller the P-value the smaller the probability that H0 is true, and therefore, the smaller the probability of making a type I error. Considering this, it has been agreed that the risk (probability) of type I error should be the determining factor in ...

#### Solution Summary

The detailed explanation to the posted question is given in the attached file. Please download the attached file DQ+1(answers).doc for detailed explanation.