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I have done rudimentary (i.e. stat class) hypothesis testing. But I currently have a question that is phrased as follows

Calculate at the 5% level of whether the mean algebra score in schools with average class sizes less than or equal to 25 students the mean algebra score in schools with average class sizes greater than 25 students. Formally state the null hypothesis in terms of population level conditional expectations.

My Questions:

How can one use conditional expectations for hypothesis testing?

Stan Shunpike
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1 Answers1

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Conditional expectations mean that if one result is found, it is likely that another has occurred or will occur. This is expressed as:

P(A|B) for the probabilities of A, given B.

The null hypothesis is a possible result, hopefully rejected to support the claim that if B will occur, A is likely.

The population in your example is a class of students, within a 5% confidence interval that those in a sample size of 25 students on average, have the average algebra test scores. And then, if class sizes greater than 25 students have the mean test scores (average scores) just as the class of 25 students does.

Therefore, given the probability of a sample size less than or equal to 25, and the sample size greater than 25, can you reject the null hypothesis for the corresponding confidence interval?

This might help: Z-Curves