Question

Fictitious Scenario
Suppose you perform a hypothesis test relating to environmental toxins in a thriving small city in West Virginia. Environmental toxins are at a safe level if they are rated at a score of 10 or fewer. A score above 10 indicates an unsafe toxin level - a level at which doctors believe people will develop health problems, diseases, and early death.

Most of the residents who live there work in coal mines and currently this is the only place left to do this type of work in the U.S. The workers have been doing this for generations and have few other skills. They are happy; they raise families there and the city used to be known as one of the best places to live and bring up children.

Ho: Toxins less than or equal to 10 (Safe)
Ha: Toxins are greater than 10 (Unsafe)

Posting Assignment
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Discuss the risk to all interested parties in the scenario if you make a Type I error and if you make a Type II error.

Answer 1

Type I error means rejecting the null hypothesis Ho, even if it is true.
On the other hand, type II error means null hypothesis is accepted even though it is false.

The two hypothesis considered here are:
Ho: Toxins less than or equal to 10 (Safe)
Ha: Toxins are greater than 10 (Unsafe)

So when type I error occurs then we reject the null hypothesis that toxin level is less than or equal to 10 (though it is true).
A score above 10 indicates an unsafe toxin level - a level at which doctors believe people will develop health problems, diseases, and early death.
That is we consider the place to be unsafe when in actual it is safe. That is the people residing there might just decide to move onto some place else. Since most of the people are workers in coal mines, the coal industry would suffer as a result. Also this is the only place in US for such type of work and in long run the country would suffer as well. It is told that the residents do not have any other special skill it would be hard for them to find a job someplace else and in some other sector. Thus their way of living would follow a downward trend. West Virginia would no longer be termed as one of the best places to live and bring up children, although in actual there is nothing wrong with the place and it's toxic level.

On the other hand when type II error occurs then we accept the null hypothesis that that toxin level is less than or equal to 10 (when in actual it is false). That is we consider the place to be safe when in actual it is unsafe.
A score above 10 indicates an unsafe toxin level - a level at which doctors believe people will develop health problems, diseases, and early death.
As a result the people residing in West Virginia would face many health issues without knowing the exact reason. The mortality rate would also increase henceforth. And we know the coal industry of West Virginia is mainly run by the local residents. As a result the labour sector will be affected in the long run, indirectly affecting the output of the industry and hence the economy level of U.S.(since,urrently this is the only place left to do this type of work in the U.S.)

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