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这是名字 · 2025年07月02日

检验统计量

NO.PZ2024120401000068

问题如下:

We regressed a security's returns, S(i), against market index returns, M(i), in order to estimate the security's beta according to R(i) = intercept + beta*M(i). The sample size is 48. The regression output is: R(i) = 0.020 + 1.080*M(i). The standard error of the intercept, SE(intercept), is 0.030; the standard error of the beta, SE(beta), is 0.050. The two-sided null hypothesis is that the security's beta is one; i.e., the null is beta = 1.0. Can we reject the null at 95% confidence?

选项:

A.

No, the t-statistic is 1.60

B.

No, the t-statistic is 21.60

C.

Yes, the t-statistic is 5.85

D.

Yes, the t-statistic is 21.60

解释:

t-statistic = (1.08 - 1.0)/0.05 = 1.60.

As the t-statistic does not exceed the two-sided 95% critical value of 1.96, we do not reject the null; i.e., the population beta may be 1.0. Sample size is not required, it informs the given standard error. We only need to see that the sample is large to realize the t-statistic is approximately normal.

Please note that, if the null hypothesis were "the slope is zero," then the t-statistic is (1.08 - 0)/0.05 = 21.60, and we would reject that null.

通过此题想明确一个概念:

无论是Z分布还是t分布,我们用“(样本均值-总体均值)/标准差” (此题套用(b-u0)/sigmab) 计算得到的是检验统计量(test statistical),用检验统计量跟critical value比较,如果检验统计量小于critical value,则无法拒绝原假设;若大于则拒绝。

此概念应该是正确的吧。

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NO.PZ2024120401000068问题如下 We regressea security's returns, S(i), against market inx returns, M(i), in orr to estimate the security's beta accorng to R(i) = intercept + beta*M(i). The sample size is 48. The regression output is: R(i) = 0.020 + 1.080*M(i). The stanrerror of the intercept, SE(intercept), is 0.030; the stanrerror of the betSE(beta), is 0.050. The two-sinull hypothesis is ththe security's beta is one; i.e., the null is beta = 1.0. Cwe rejethe null 95% confince? A.No, the t-statistic is 1.60 B.No, the t-statistic is 21.60C.Yes, the t-statistic is 5.85 Yes, the t-statistic is 21.60 t-statistic = (1.08 - 1.0)/0.05 = 1.60. the t-statistic es not exceethe two-si95% criticvalue of 1.96, we not rejethe null; i.e., the population beta m1.0. Sample size is not require it informs the given stanrerror. We only neeto see ththe sample is large to realize the t-statistic is approximately normal. Please note that, if the null hypothesis were \"the slope is zero,\" then the t-statistic is (1.08 - 0)/0.05 = 21.60, anwe woulrejethnull. 该题目计算的t为1.6,置信区间为1±0.05*1.96,然而临界值1.96

2025-06-19 16:36 1 · 回答

NO.PZ2024120401000068问题如下 We regressea security's returns, S(i), against market inx returns, M(i), in orr to estimate the security's beta accorng to R(i) = intercept + beta*M(i). The sample size is 48. The regression output is: R(i) = 0.020 + 1.080*M(i). The stanrerror of the intercept, SE(intercept), is 0.030; the stanrerror of the betSE(beta), is 0.050. The two-sinull hypothesis is ththe security's beta is one; i.e., the null is beta = 1.0. Cwe rejethe null 95% confince? A.No, the t-statistic is 1.60 B.No, the t-statistic is 21.60C.Yes, the t-statistic is 5.85 Yes, the t-statistic is 21.60 t-statistic = (1.08 - 1.0)/0.05 = 1.60. the t-statistic es not exceethe two-si95% criticvalue of 1.96, we not rejethe null; i.e., the population beta m1.0. Sample size is not require it informs the given stanrerror. We only neeto see ththe sample is large to realize the t-statistic is approximately normal. Please note that, if the null hypothesis were \"the slope is zero,\" then the t-statistic is (1.08 - 0)/0.05 = 21.60, anwe woulrejethnull. 是不是回归检验算出来的都叫t统计量,但是n>30可以当成正态分布所以不用查表也能判断

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