Example: t-distribution vs z-distributionIf you measure the average test score from a sample of only 20 students, you should use the t-distribution to estimate the confidence interval around the mean. This means that it gives a lower probability to the center and a higher probability to the tails than the standard normal distribution. It is a more conservative form of the standard normal distribution, also known as the z-distribution. The variance in a t-distribution is estimated based on the degrees of freedom of the data set (total number of observations minus 1). The t-distribution is used when data are approximately normally distributed, which means the data follow a bell shape but the population variance is unknown. Normally-distributed data form a bell shape when plotted on a graph, with more observations near the mean and fewer observations in the tails. The t-distribution is a type of normal distribution that is used for smaller sample sizes. Frequently asked questions about the t-distribution.T-distribution and the standard normal distribution.
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