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?
选项:
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 and so = 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 =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
CI corresponds to the point where there is 0.5% in each tail, or 2.57。
样本置信区间求总体均值,首先根据对称性求得样本均值,由于总体方差和样本容量未知,所以用t分布,由于置信区间是99%,所以α=0.5。这样理解对吗?但是之后怎么求2.57呢?