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Stats Questions on t-tests

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1. Why do you use N-1 rather than just N when calculating the standard deviation as estimated from a sample? How does the t-statistic differ from the z-statistic? When would you use a single-sample t-test?

2. What is an independent-sample test? How does it differ from a single-sample t-test and a paired-sample test?Why do you need to calculate the pooled variance in an independent-sample t-test?

3. Why do you need to calculate the pooled variance in an independent-samples t-test?

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This solution answers various questions related to statistics and hypothesis testing.

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1. Why do you use N-1 rather than just N when calculating the standard deviation as estimated from a sample? How does the t-statistic differ from the z-statistic? When would you use a single-sample t-test?

This is because the standard deviation of the entire population is unknown, so instead you use the standard deviation of the sample. The formula for the sample standard deviation is (see attachment) and you divide by (N-1) instead of N because the sample standard deviation is used for the corrected estimator while the population standard deviation is used for the uncorrected estimator. This correction for the sample standard deviation is ...

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