Probstat/notes/t-distributions

จาก Theory Wiki
ไปยังการนำทาง ไปยังการค้นหา
This is part of probstat.

In many applications including computing confidence intervals and also hypothesis testing, we need to know the distribution of the sample mean. Let be a sample mean of a normal population computed from a sample of size . If the variance of the population is known, we have that

However, in most cases, we do not know and we only have the sample variance

.

Therefore, we would like to use the sample standard deviation instead of the real standard deviation . We hope that

will be close to normal. This is indeed true. Although is not normal, it is t-distributed with degree of freedom. (See definition below.) Therefore, we can use the table for the t-distribution to compute probabilities for various events related to this statistic.

We will show example usages for the t-distributions and then discuss the mechanics behind this usage of the t-distribution.

EX1:


Student's t-Distribution