Degrees of freedom refer to the number of independent values or quantities which can be assigned to a statistical distribution. They are crucial in estimating population parameters and conducting hypothesis tests.
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Degrees of freedom (df) for a single sample t-test is calculated as $n-1$, where $n$ is the sample size.
In confidence intervals, degrees of freedom affect the critical value from the t-distribution table.
When calculating confidence intervals for small samples with unknown population standard deviation, degrees of freedom determine the shape of the t-distribution.
Higher degrees of freedom result in the t-distribution approaching a normal distribution.
In paired sample tests, degrees of freedom are calculated as $n-1$, where $n$ is the number of pairs.
Review Questions
How do you calculate degrees of freedom for a single sample t-test?
Why are degrees of freedom important in determining the critical value in confidence intervals?
What effect do higher degrees of freedom have on the shape of the t-distribution?
Related terms
t-Distribution: $t$-distribution is a type of probability distribution that is symmetric and bell-shaped but has heavier tails than the normal distribution. It is used when estimating population parameters with small sample sizes.
Confidence Interval: A range around a sample statistic that provides an estimated range where a population parameter lies, based on a specific level of confidence.
Population Standard Deviation: $\sigma$ (sigma) represents how data points in an entire population differ from the mean. When unknown, it is estimated using sample data.