Survey

Survey

Document related concepts

Transcript

The t-Distribution Characteristics From [Blu4 page 358] and [JK10 page 476] How the t-Distribution is similar to the Standard Normal Distribution It is bell-shaped It is symmetric about the mean The mean, median, and mode are all equal to 0 The mean, median, and mode are all located at the center of the distribution The curve never touches the x-axis. How it differs from the Standard Normal Distribution It is not quite as peaked as the Normal Distribution There’s more thickness in the tails of the tDistribution The variance is greater than 1 It’s a family of distributions, a different distribution for each degrees of freedom number The variance is greater than 1 but as the degrees of freedom increases, the variance approaches 1, and the t-Distribution approaches the standard Normal Distribution Graphing [to be done later – good pictures in [JK10 page 476] and [Blu4 page 358] Advanced - the formula [To be obtained from Burington & May or other advanced text] What is Degrees of Freedom, df? [Blu4 page 358] The degrees of freedom are the number of values that are free to vary after a sample statistic has been computed. Example: five values and the mean is 10. Four of the five values are free to vary. Once four values have been chosen, the fifth value is locked in. [JK10 page 476] The sample variance is the mean of the squared deviations, ∑(𝑥−𝑥̅ )2 𝑛−1 but we are constrained by ∑(𝑥 − 𝑥̅ ) = 0, the sum of the deviations must be zero. Only the first 𝑛 − 1 of these deviations has freedom of value. Cases where 𝑑𝑓 = 1 or 𝑑𝑓 = 2 are special and ordinarily we won’t consider nor encounter such cases. Document1 4/30/2017 4:30 AM