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"The t-distribution has the following properties: i) The t-distribution is bell-shaped and symmetric about the value t = 0, ranging from – ∞ to ∞. ii) The number of degrees of freedom determines the shape of the t-distribution. Thus there is a different t-distribution for each number of degrees of freedom. As such, it is a whole family of distributions. The t-distribution, for small values of ν, is flatter than the standard normal distribution which means that the t distribution is more spread out in the tails than is the standard normal distribution. As the degrees of freedom increase, the tdistribution becomes narrower and narrower, until, as n tends to infinity, it tends to coincide with the standard normal distribution. (The t-distribution can never become narrower than the standard normal distribution.) iii) The t-distribution has a mean of zero, when ν ≥ 2. (The mean does not exist when ν = 1.) iv) The median of the t-distribution is also equal to zero. docsity.com v) The t-distribution is unimodal. The density of the distribution reaches its maximum at t = 0 and thus the mode of the t- distribution is t = 0. (The students will recall that, for any hump-shaped symmetric distribution, the mean, median and mode are equal.) Source: http://in.docsity.com/en-docs/T_Distribution-Statistics-Solved_Quizes_"

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