Statistics 简明教程
Statistics - Student T Test
T 检验是小样本检验。它由威廉·戈塞特于 1908 年制定。他以“学生”的笔名发表了此项检验。因此，它被称为学生的 t 检验。要应用 t 检验，需计算 t 统计量。为此，请使用以下公式：
T-test is small sample test. It was developed by William Gosset in 1908. He published this test under the pen name of "Student". Therefore, it is known as Student’s t-test. For applying t-test, the value of t-statistic is computed. For this, the following formula is used:
Formula
Example
Problem Statement:
Problem Statement:
9 个来自普通人群的质量样本的均值为 41.5 英寸，与该均值相等的偏差平方和为 72 英寸。说明人群中均值 44.5 英寸的假设是否合理（对于 ${v}={8},\ {t_.05}={2.776}$）。
An irregular sample of 9 qualities from an ordinary populace demonstrated a mean of 41.5 inches and the entirety of square of deviation from this mean equivalent to 72 inches. Show whether the supposition of mean of 44.5 inches in the populace is reasonable.(For ${v}={8},\ {t_.05}={2.776}$)
Solution:
Solution:
我们假设零假设是总体均值为 44.5。
Let us take the null hypothesis that the population mean is 44.5.
应用 t 检验：
Applying t-test:
自由度 = $ {v = n-1 = 9-1 = 8 }$. 对于 ${v = 8, t_{0.05}}$，双尾检验为 ${2.306}$。由于 {|t|} 的计算值 > {t} 的表值，我们否定零假设。我们得出结论：总体均值不等于 44.5。
Degrees of freedom = $ {v = n-1 = 9-1 = 8 }$. For ${v = 8, t_{0.05}}$ for two tailed test = ${2.306}$. Since, the calculated value of $ {|t|}$ > the table value of $ {t}$, we reject the null hypothesis. We conclude that the population mean is not equal to 44.5.