When applying statistical tests involving comparing two means or a sample to a p
ID: 3180064 • Letter: W
Question
When applying statistical tests involving comparing two means or a sample to a population mean, there are many organizational applications. For example, Human Resources may want to track entrance exam scores of their new hires. This would be an example of two mean comparison. In terms of the recent election, Gallup may take a sample and compare to a population of candidate votes (sample mean compared to a population mean).
Think of an example in your organization of either one of these tests and discuss its application as well as the risk of type 1 or 2 errors.
Explanation / Answer
In a pharmaceutical company, a medical researcher wants to compare the effectiveness of two medications. The null and alternative hypotheses are:
Null hypothesis (H0): 1= 2
The two medications are equally effective.
Alternative hypothesis (H1): 1 2
The two medications are not equally effective.
A type I error occurs if the researcher rejects the null hypothesis and concludes that the two medications are different when, in fact, they are not. If the medications have the same effectiveness, the researcher may not consider this error too severe because the patients still benefit from the same level of effectiveness regardless of which medicine they take. However, if a type II error occurs, the researcher fails to reject the null hypothesis when it should be rejected. That is, the researcher concludes that the medications are the same when, in fact, they are different. This error is potentially life-threatening if the less-effective medication is sold to the public instead of the more effective one.
As you conduct your hypothesis tests, consider the risks of making type I and type II errors. If the consequences of making one type of error are more severe or costly than making the other type of error, then choose a level of significance and a power for the test that will reflect the relative severity of those consequences.
TY!
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