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VincentShell · 2022年12月14日

老师关于t的df怎么算？

  1. CFA I
  2. Quantitative

NO.PZ2015120604000137

问题如下：

Ida Lee and his team collect a lot of analysis of statistical data about the car market .According to the data, they come to the conclusion that the mean price of SUV is more than $46,435 in his country. Then they randomly select 64 SUVs whose mean price is $46,760. Assuming the standard deviation of the sample is 1370. Ida Lee conducts a hypothesis test to check their conclusion. At which significant level should Ida Lee reject the null hypothesis?

选项：

A.

0.5%.

B.

5%.

C.

1%.

解释：

B is correct.

If the significant level is 5%, the critical value=1.669<1.8978, Ida Lee should reject the null.

If the significant level is 0.5%, the critical value=2.656>1.8978, Ida Lee will fail to reject the null.

If the significant level is 1%, the critical value=2.387>1.8978, Ida Lee will fail to reject the null.


在A选项中为什么t=64而不是t=64-2？差的t表格差了一些

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星星_品职助教 · 2022年12月15日

同学你好，

df都是源自于数学证明，即经过自由度调整过后的估计量可以满足无偏性。

从考试的角度，需要记忆不同场景下的自由度情况，本题为检验均值和一个确定性的数字之间关系，对应的df就是n-1.

--------

教材上有一张关于test statistic和df总结的表格，可以用来做参考。

后面还会学到一元回归系数的t检验，df=n-2，可以补充在一起。

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