In general, the t test for correlated groups is a more powerful test than the sign test. Is this statement true? Explain why? Can you think of situations in which the sign test might be more powerful than the t test for correlated groups (assume N is the same for both tests, etc.)?

nicekikah 2020-12-24 Answered
In general, the t test for correlated groups is a more powerful test than the sign test. Is this statement true? Explain why? Can you think of situations in which the sign test might be more powerful than the t test for correlated groups (assume N is the same for both tests, etc.)?
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smallq9
Answered 2020-12-25 Author has 106 answers
From the given information, the statement is “the t test for correlated groups is a more powerful test than the sign test”.
In general, the sign test is more powerful than the correlated t test.
Hence, the given statement is false.
Example for sign test:
Claim: Testing whether the two populations have same median sales or not.
Sales data:
Sales after: 615,157,793,287,718.
Sales before: 467,214,647,259,683.
Example for t test for correlated groups test:
Claim: Testing whether the two temperatures at 8 AM and 12 AM have the same mean or not.
Data:
Temperature at 8AM:98.2,99.2,97.5,97.5,97.5
Temperature at 12AM:98.9,99.7,97.8,97.2,97.7
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