t-distributions, one and two sample t procedures, paired data and conditions for inference.
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- What is a t-distribution used for in statistics?
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Inference about population means when the population standard deviation is unknown and sample size is small- How does degrees of freedom affect the shape of a t-distribution?
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As degrees of freedom increase, the t-distribution approaches the normal distribution and tails become lighter- What does it mean that a t-distribution has 'heavier tails' than a normal distribution?
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Extreme values are more likely in a t-distribution, making it more conservative for inference- At what sample size does the t-distribution become approximately equal to the normal distribution?
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Around 30 observations or greater, though it depends on how close you need the approximation to be- What is the formula for the test statistic in a one-sample t-test?
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t = (x-bar - mu0) / (s / sqrt(n))- What are the three main conditions for performing a t-test?
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1) Random sample or random assignment, 2) Independence of observations, 3) Data approximately normal or large sample size- What is the degrees of freedom for a one-sample t-test?
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n - 1, where n is the sample size- What is the standard error in a one-sample t-test?
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s / sqrt(n), where s is the sample standard deviation and n is the sample size- What is the formula for a confidence interval for a population mean using t?
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x-bar +/- t* (s / sqrt(n))- When should you use a t-test instead of a z-test?
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When the population standard deviation is unknown and must be estimated from the sample- What is a paired t-test?
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A test for comparing two related samples where each observation in one sample is paired with an observation in the other- How do you set up data for a paired t-test?
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Calculate the difference between paired observations, then treat the differences as a single sample- What is the degrees of freedom for a paired t-test?
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n - 1, where n is the number of pairs- What is the formula for the test statistic in a two-sample unpooled t-test?
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t = (x1-bar - x2-bar) / sqrt(s1^2/n1 + s2^2/n2)- What is a pooled t-test and when should you use it?
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A two-sample t-test that assumes equal population variances and pools the sample variances; use when you have evidence variances are equal
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