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How does the sample size impact the t-test?

How does the sample size impact the t-test?

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Answer #1

The t distribution has heavier tails than the normal distribution the comparable critical value will be larger in absolute value than for the standard normal distribution. But the distribution will converge to the normal as the degrees of freedom (n-1 in your example) increase.

In t-test, the t statistic is :

Increasing n will result in a sample mean closer to the population mean, but only in the case that your sample is not different from the population. So when n is high and still differs from μ, that reinforces the rejection of the null hypothesis.

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