A large manufacturing firm is being charged with discrimination in its hiring practices. a. What hypothesis is being tested if a jury commits a type I error by finding the firm guilty? b. What hypothesis is being tested if a jury commits a type II error by finding the firm guilty?

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Mathematics

Paul

26 February, 10:33

A large manufacturing firm is being charged with discrimination in its hiring practices. a. What hypothesis is being tested if a jury commits a type I error by finding the firm guilty? b. What hypothesis is being tested if a jury commits a type II error by finding the firm guilty?

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Christopher · Answer 1

a) From the definitions above we see that a type of error I is when we reject a null hypothesis when is really true.

So then on this case the type of error I would be reject the hypothesis that the firm is not guilty when is really not guilty.

b) A type of error II occurs when we no reject a false null hypothesis.

And for this case would be find the firm guilty but we fail to reject the hypothesis that is not guilty.

Step-by-step explanation:

Previous concepts

A hypothesis is defined as "a speculation or theory based on insufficient evidence that lends itself to further testing and experimentation. With further testing, a hypothesis can usually be proven true or false".

The null hypothesis is defined as "a hypothesis that says there is no statistical significance between the two variables in the hypothesis. It is the hypothesis that the researcher is trying to disprove".

The alternative hypothesis is "just the inverse, or opposite, of the null hypothesis. It is the hypothesis that researcher is trying to prove".

Type I error, also known as a "false positive" is the error of rejecting a null hypothesis when it is actually true. Can be interpreted as the error of no reject an alternative hypothesis when the results can be attributed not to the reality.

Type II error, also known as a "false negative" is the error of not rejecting a null hypothesis when the alternative hypothesis is the true. Can be interpreted as the error of failing to accept an alternative hypothesis when we don't have enough statistical power

Solution to the problem

The system of hypothesis on this case would be:

Null: Firm is not guilty

Alternative: Firm is guilty

Part a

From the definitions above we see that a type of error I is when we reject a null hypothesis when is really true.

So then on this case the type of error I would be reject the hypothesis that the firm is not guilty when is really not guilty.

Part b

A type of error II occurs when we no reject a false null hypothesis.

And for this case would be find the firm guilty but we fail to reject the hypothesis that is not guilty.