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Pina · 2020年07月26日

问一道题：NO.PZ2015120204000014

  1. CFA II
  2. Quantitative

问题如下：

Based on past research, Hansen selects the following independent variables to predict IPO initial returns:

Underwriter rank = 1–10, where 10 is highest rank

Pre-offer price adjustment (Expressed as a decimal) = (Offer price – Initial filing price)/Initial filing price

Offer size ($ millions) = Shares sold × Offer price

Fraction retained (Expressed as a decimal) = Fraction of total company shares retained by insiders

Hansen collects a sample of 1,725 recent IPOs for his regression model.

\Hansen’s Regression Results Dependent Variable: IPO Initial Return (Expressed in Decimal Form, i.e., 1% = 0.01)

The 95 percent confidence interval for the regression coefficient for the pre-offer price adjustment is closest to:

选项：

A.

0.156 to 0.714.

B.

0.395 to 0.475.

C.

0.402 to 0.468.

解释：

B is correct.

The 95% confidence interval is 0.435 ± (0.0202 × 1.96) = (0.395, 0.475).

老师好 查表得T critical 的时候怎么判断alpha = 0.05 or 0.025? 在求confidence interval 的时候。 假设检验的时候是看Ha 的是吗? Ha 中的是> 那么拒绝区域就在图的右边 如果小于， 拒绝区域在图的左边， 如果是不等于， 那就是两边（双尾） 也就是IF ALPHA =0.05, 那我们查表格的时候就看alpha = 0.025 是吗？ 然后等号永远在原假设里的是吗 ?谢谢

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星星_品职助教 · 2020年07月26日

同学你好，

confidence interval是分布中间的那块区域，所以对应着分布两边各有一块“尾巴”，所以例如本题95%confidence interval，对应的就是5%的significance level，这5%就是双尾的总面积，如果查双尾t表，就直接查5%，但如果是单尾t表（例如原版书附录表），就要查单尾2.5%的情况。

如果是假设检验的题型，要看备择假设，例如备择假设是Ha：b1≠0，那么就要想到不等于0是包含两种情况的：远大于0和远小于0，所以就是两边各有一个拒绝域，无论是以上哪种情况都可以拒绝等于0的原假设。还以α=0.05为例，同样如果查双尾t表，就直接对应双尾总面积为5%对应的t critical value，如果是单尾t表，就要查单尾2.5%的情况 。

如果Ha为b1＞0，那么拒绝域就在右尾。这个时候如果α=5%，那就要查单尾t表面积为5%的情况，这个时候不存在双尾。

同理，备择假设是b1＜0则拒绝域在左尾。这个时候如果α=5%，依然要查单尾t表面积为5%的情况，只不过此时得到的critical value值要加上负号。

等号在原假设里。有一个简单的记忆方法，因为绝大多数原假设都是H0：b1=0，通过这个可以记忆等号位置一定放在原假设，但这是一级考点，二级考察的并不是很多。

苟 · 2020年11月06日

请问老师，怎么判断这道题是该用单尾还是双尾？

星星_品职助教 · 2020年11月07日

@苟

confidence interval是分布中间的那块区域，所以对应着分布两边各有一块“尾巴”，即双尾

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