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上小学 · 2023年03月26日

题样本均值不就是2,32吗?12,78开根号就是样本均值的标准误已经给定了?把均值和方差加起来除以2?37年的数据为啥还开根号?

NO.PZ2020010304000050

问题如下:

If you are given a 99% confidence interval for the mean return on the Nasdaq 100 of [2.32%, 12.78%], what is the sample mean and standard error? If this confidence interval is based on 37 years of data, assumed to be iid, what is the sample standard deviation?

解释:

The mean is the midpoint of a symmetric confidence interval (the usual type), and so is 7.55%.

The 99% CI is constructed as [μcσ,μ+cσ]\left[\overset\wedge\mu-c*\overset\wedge\sigma, \overset\wedge\mu+c*\overset\wedge\sigma\right] and so cσc*\overset\wedge\sigma = 12.78% - 7.55% = 5.23%. The critical value for a 99% CI corresponds to the point where there is 0.5% in each tail, or 2.57, and so σ\overset\wedge\sigma =5.23% /2.57=2.03% needs to be surveyed.

If this confidence interval is based on 37 years of data, assumed to be iid, the sample standard deviation is 2.03%×37=12.34%2.03\%\times\sqrt{37}=12.34\%

此题已经给定均值方差,解题思路不明。

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品职答疑小助手雍 · 2023年03月26日

同学你好,读题错误,题目第一句说的是confidence interval 是[2.32%, 12.78%],interval指的是一个区间范围,不是指分布的均值方差属性。

上小学 · 2023年03月27日

通过做题已经得出正确答案,谢谢!

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NO.PZ2020010304000050问题如下If you are given a 99% confinintervfor the mereturn on the Nasq 100 of [2.32%, 12.78%], whis the sample meanstanrerror? If this confinintervis baseon 37 years of tassumeto ii whis the sample stanrviation? The meis the mioint of a symmetric confininterv(the usutype), anso is 7.55%.The 99% is constructe[μ∧−c∗σ∧,μ∧+c∗σ∧]\left[\overset\wee\mu-c*\overset\wee\sigm\overset\wee\mu+c*\overset\wee\sigma\right][μ∧​−c∗σ∧,μ∧​+c∗σ∧] anso c∗σ∧c*\overset\wee\sigmac∗σ∧ = 12.78% - 7.55% = 5.23%. The criticvalue for a 99% correspon to the point where there is 0.5% in eatail, or 2.57, anso σ∧\overset\wee\sigmaσ∧ =5.23% /2.57=2.03% nee to surveye If this confinintervis baseon 37 years of tassumeto ii the sample stanrviation is 2.03%×37=12.34%2.03\%\times\sqrt{37}=12.34\%2.03%×37​=12.34%我的问题在直接用2.58倍的viation算吗 为什么都没有用到u

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