ผลต่างระหว่างรุ่นของ "Probstat/notes/t-distributions"

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will be close to normal.  This is indeed true.  Although <math>\sqrt{n}(\bar{X}-\mu)/S</math> is not normal, it is ''t''-distributed with <math>n-1</math> 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.   
 
will be close to normal.  This is indeed true.  Although <math>\sqrt{n}(\bar{X}-\mu)/S</math> is not normal, it is ''t''-distributed with <math>n-1</math> 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.   
  
== t-Distribution ==
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== Student's ''t''-Distribution ==

รุ่นแก้ไขเมื่อ 14:02, 5 ธันวาคม 2557

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.

Student's t-Distribution