Let\'s say that you want to do a study of the possible relationship between gend
ID: 3172601 • Letter: L
Question
Let's say that you want to do a study of the possible relationship between gender and GPA. You enlist the help of 100 friends that all attend different colleges/universities. Each of your friends conducts their own study at their school, where they ask 30 males and 30 females their GPA. They then do a t-test on the data. 95 of your friends come back and say that found no significant difference between gender and GPA. However, 5 friends come back and say they did find a significant difference, such that males or females had significantly higher GPA than the opposite sex.
What do you make of these last 5 surveys? Is it evidence that males and females have different GPA's? Why or why not? (Note: consider all 100 surveys in your answer and consider the theory in terms of the generation of the F-distribution and P-values).
Explanation / Answer
Only 5% of the surveys showed that there is a difference in the GPA's of males and females. When we construct a 5% rejection region for a test, we mean that approximately in 5% cases of the experiment we will end up rejecting the null hypothesis even when it is true. Here if the null hypothesis is that males and females have differnt GPAs, we have rejected the null hypothesis in 5% cases, this can happen by chance of randomness even when the null hypothesis is true. So we can disregard the 5% cases and conclude males and females have similar GPAs.
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