1.) Why do we have to use a "t-test" instead of a "z-test" for a claim about two mean? 2.) In your own words, what does it mean to have a "paired" sample? Give an example that is not in the book, online or given in class. 3.) How do you figure the number of degrees of freedom for a test of two independent means?
1.) Both the 't-test' and the 'z-test' are symmetrical and are used for testing the means of a population.
In case of a claim about means, both t-test and z-test are used depending on which parameter is known and which is unknown. Usually the population standard deviation is unknown so an estimate of population standard deviation is used and hence instead of z-test, t-test is applied.
It's a case of two sample, and the population standard deviation is unknown, so a t-test will be applied using the formula :
2.) A "paired" sample is the one in which out of the two samples, the observations of one sample are related to the observations of another sample. There are various examples of the paired sample like,
- To test the impact of a medicine before and after it's use.
-To test how well students score on an exam before and after studying.
- To test the weight loss before and after having green tea.
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