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查Z或T表

NO.PZ2015120204000022

问题如下：

${l}Excess\text{ }stock\text{ }market\text{ }return_t\\=a_0+a_1Default\text{ }spread_{t-1}\text{ }+a_2Term\text{ }spread_{t-1}\text{ }+a_3Pres\text{ }party\text{ }dummy_{t-1}\text{ }+e$

Default spread is equal to the yield on Baa bonds minus the yield on Aaa bonds. Term spread is equal to the yield on a 10-year constant-maturity US Treasury index minus the yield on a 1-year constant-maturity US Treasury index. Pres party dummy is equal to 1 if the US President is a member of the Democratic Party and 0 if a member of the Republican Party.

The regression is estimated with 431 observations.

Exhibit 1.Multiple Regression Output

Exhibit 2. Table of the Student’s t-Distribution (One-Tailed Probabilities for df = ∞)

The 95 percent confidence interval for the regression coefficient for the default spread is closest to:

选项：

0.13 to 5.95.

1.72 to 4.36.

1.93 to 4.15.

解释：

B is correct.

The confidence interval is computed as $a_1\pm s(a_1)\times(95\%,\infty)$ . From Exhibit 1, a₁ = 3.04 and t(a₁) = 4.52, resulting in a standard error of a₁ = s(a₁) = 3.04/4.52 = 0.673. The critical value for t from Exhibit 3 is 1.96 for p = 0.025. The confidence interval for a₁ is 3.04 ± 0.673 × 1.96 = 3.04 ± 1.31908 or from 1.72092 to 4.35908.

老师，本题因为我看统计量大于30，所以直接用了Z-TEST对应的95%概率区间的1.96，没有参照题目给出T-TEST对应的值，但也做对了，这个是巧合吗，之后也可以这么做吗（看到统计量大于30就用Z-TEST）

同学你好，

用z值去替代t值是一种近似的方法。所以：

①如果涉及到精细计算的题目，不能近似替代，此时需要查表找精确的t值。

本题可以直接使用1.96的原因在于题目中的“Exhibit 2”要求就按照1.96来做计算。但如果不给这个条件的话，t的关键值是比对应的z值大的，此时如果还按照z值去计算置信区间的话，就会得不到答案。

②如果只涉及大概判断，例如判断是否拒绝原假设，这种情况下直接用z的关键值去和计算出来的t统计量比较就可以。可以省去查t表找t关键值的时间。这是因为z值和t值差距非常小，选项不会在零点零几的小数位上去做文章。

查Z或T表

1 个答案

1

0

431

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