03 // 双向 STEM 与金融计算器 // 统计推断、概率分布与风险指标计算器t = (x̄ - μ₀) / (s / √n)

单样本 t 检验统计量计算器

利用 t = (x̄ - μ₀) / (s / √n) 求解学生 t 统计量、样本均值 x̄、原假设均值 μ₀、样本标准差 s 或样本量 n。

t = (x̄ - μ₀) / (s / √n)
选择要计算的未知量(或直接在任意输入框中输入数值):当前求解: t — Student's t-Statistic
计算结果

Test statistic on t-distribution with df = n - 1

-1515
unit

Arithmetic mean of the sample

-10,000.0010,000.00
unit

Benchmark mean under H₀

-10,000.0010,000.00
unit

Bessel-corrected sample standard deviation

0.015,000.00
unit

Number of observations (Degrees of Freedom df = n - 1)

2100,000.00
unit
计算结果 · Student's t-Statistic (t)
2.5

分步代入计算过程

01Canonical Law: t = (x̄ - μ₀) / (s / √n)
02Given Inputs (Base Units): x̄ = 105, μ₀ = 100, s = 10, n = 25
03Solve for t (Student's t-Statistic): t = 2.5

Student's one-sample t-test evaluates how many standard errors the observed sample mean x̄ lies away from the hypothesized null population mean μ₀ with (n - 1) degrees of freedom.

常见参考标准值

Critical t (df = 24, α = 0.05 Two-Tailed)|t| ≥ 2.0639

Rejects H₀ at 95% confidence level

Critical t (df = 24, α = 0.01 Two-Tailed)|t| ≥ 2.7969

Rejects H₀ at 99% confidence level

Large-Sample Gaussian Limit (df → ∞)t* → z* = 1.9600

Converges to standard normal Z-distribution

20 行数值对照表

Student's t-Statistic (t) · Observed Sample Mean (x̄)

One-Sample Student's t-Statistic Calculator — Observed Sample Mean → Student's t-Statistic
#Observed Sample Mean (x̄)Student's t-Statistic (t)Δ %
01-2,145.00 -1,122.50 -45000.00%
02-1,881.84 -990.9211 -39736.84%
03-1,618.68 -859.3421 -34473.68%
04-1,355.53 -727.7632 -29210.53%
05-1,092.37 -596.1842 -23947.37%
06-829.2105 -464.6053 -18684.21%
07-566.0526 -333.0263 -13421.05%
08-302.8947 -201.4474 -8157.89%
09-39.7368 -69.8684 -2894.74%
10105 当前2.5 0.00%
11486.5789 193.2895 +7631.58%
12749.7368 324.8684 +12894.74%
131,012.89 456.4474 +18157.89%
141,276.05 588.0263 +23421.05%
151,539.21 719.6053 +28684.21%
161,802.37 851.1842 +33947.37%
172,065.53 982.7632 +39210.53%
182,328.68 1,114.34 +44473.68%
192,591.84 1,245.92 +49736.84%
202,855.00 1,377.50 +55000.00%
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常见问题解答 (FAQ)

如何使用在线 单样本 t 检验统计量计算器 工具?+

输入已知参数或拖动滑块,即可在浏览器中实时计算并可视化 单样本 t 检验统计量计算器(基于关系式 t = (x̄ - μ₀) / (s / √n))。利用 t = (x̄ - μ₀) / (s / √n) 求解学生 t 统计量、样本均值 x̄、原假设均值 μ₀、样本标准差 s 或样本量 n。

可以导出或打印 单样本 t 检验统计量计算器 的结果吗?+

可以。支持一键复制数据、打印计算工作表或导出高清 SVG、PNG 和 CSV 文件。

我可以清空 单样本 t 检验统计量计算器 中的示例数据并从空白状态开始吗?+

可以。点击工具顶部的“清空 / 空白开始”按钮即可重置所有输入项,随时也可一键重新加载示例数据。