ผลต่างระหว่างรุ่นของ "Probstat/notes/t-distributions"
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Jittat (คุย | มีส่วนร่วม) (หน้าที่ถูกสร้างด้วย ': ''This is part of probstat.'' In many applications including computing confidence intervals and also hypothesis testing, we need...') |
Jittat (คุย | มีส่วนร่วม) |
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| แถว 1: | แถว 1: | ||
: ''This is part of [[probstat]].'' | : ''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. If the variance <math>\sigma^2</math> of the population is known, we have that | + | In many applications including computing confidence intervals and also hypothesis testing, we need to know the distribution of the sample mean. Let <math>\bar{X}</math> be a sample mean of a normal population computed from a sample of size <math>n</math>. If the variance <math>\sigma^2</math> of the population is known, we have that |
<center> | <center> | ||
<math> | <math> | ||
| − | \frac{\bar{X}-\mu}{\sigma} \sim Normal(0,1). | + | \frac{\bar{X}-\mu}{\sigma/\sqrt{n}} \sim Normal(0,1). |
</math> | </math> | ||
</center> | </center> | ||
รุ่นแก้ไขเมื่อ 13:56, 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
