When is it appropriate to use the t test?

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The t-test is appropriate for comparing two means when the sample size is small, typically less than 30. It assumes that the underlying data distribution is normal. Additionally, the t-test is suitable when the variances of the two groups are equal or approximately equal. It is important to verify these conditions before applying the t-test to ensure valid results. Understanding these criteria helps in making informed statistical comparisons.
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Homework Statement



If i have data and want to compare the two means, when is it appropriate to use the t test?

The Attempt at a Solution



i know its because the distribution is normal but there are also other reasons.
Thank you.
 
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the t-test is used when the sample size is "small" less than 30 and the underlying distribution is normal.
 
Question: A clock's minute hand has length 4 and its hour hand has length 3. What is the distance between the tips at the moment when it is increasing most rapidly?(Putnam Exam Question) Answer: Making assumption that both the hands moves at constant angular velocities, the answer is ## \sqrt{7} .## But don't you think this assumption is somewhat doubtful and wrong?

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