题目
Problem
An engineer is comparing the tensile strengths of steel rods made from two machines, A and B. The engineer randomly selects 8 rods from machine A and 6 rods from machine B. The tensile strengths, in appropriate units, are given in the following table.
| Machine A | 402 | 403 | 415 | 412 | 409 | 407 | 406 | 410 |
|---|---|---|---|---|---|---|---|---|
| Machine B | 401 | 398 | 395 | 397 | 410 | 405 |
You should assume that the two distributions are normal and have the same population variance.
Use a t-test at the 5% significance level to test whether there is any difference in the mean tensile strengths of steel rods from the two machines.
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题目中文翻译
一名工程师正在比较由两台机器 A 和 B 制造的钢棒的抗拉强度。该工程师从机器 A 随机选取 8 根钢棒，从机器 B 随机选取 6 根钢棒。抗拉强度（单位适当）如下表所示。
| 机器 A | 402 | 403 | 415 | 412 | 409 | 407 | 406 | 410 |
|---|---|---|---|---|---|---|---|---|
| 机器 B | 401 | 398 | 395 | 397 | 410 | 405 |
你应假设这两个分布均为正态分布，并且具有相同的总体方差。
在 5% 显著性水平下使用 t 检验，检验来自两台机器的钢棒平均抗拉强度是否存在差异。