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real__yu · 2025年02月06日

请问1.96是哪里得来的?

NO.PZ2022062760000013

问题如下:

An analyst is testing a hypothesis that the beta, 𝛽, of stock CDM is 1. The analyst runs an ordinary least squares regression of the monthly returns of CDM, RCDM, on the monthly returns of the S&P 500 Index, Rm, and obtains the following relation:


The analyst also observes that the standard error of the coefficient of Rm is 0.80. In order to test the hypothesis H0: 𝛽 = 1 against H1: 𝛽 ≠ 1, what is the correct statistic to calculate?

选项:

A.

t-statistic

B.

Chi-squared test statistic

C.

Jarque-Bera test statistic

D.

Sum of squared residuals

解释:

中文解析:

t检验值:


因为 t<1.96,所以不能拒绝原假设。

The correct test answer is A.

The t-statistic is defined by


In this case t = -0.175. Since |t| < 1.96 we cannot reject the null hypothesis.

1.96是哪儿里得来的?

1 个答案

李坏_品职助教 · 2025年02月06日

嗨,爱思考的PZer你好:


1.96是95%置信度下的标准正态分布Z值。在进行假设检验(hypothesis test)的时候,95%是最常见的置信度。t检验可以近似看做正态分布,所以可以直接把t统计量去和1.96这个Z值进行比较,当t的绝对值大于1.96时,才能拒绝原假设。

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