题目
For a sample size of 65 with a mean of 31 taken from a normally distributed population with a variance of 529, a 99% confidence interval for the population mean will have a lower limit closest to:
选项
A.23.64.
B.25.41.
C.30.09.
答案
A
解析
A is correct. To solve, use the structure of Confidence interval = Point estimate ± Reliability factor × Standard error, which, for a normally distributed population with known variance, is represented by the following formula:「huixue_img/importSubject/1564548696392208384.png」 A正确。 置信区间=点估计±置信因子×标准误差，对于方差已知的正态分布总体，置信区间为: 样本均值±Z(a/2)*σ/(n^0.5) 在99%置信区间下，用z(0.005) = 2.58。 同时,σ= 529^0.5 = 23。 因此，下限= 31-2.58*23/(65^0.5)=23.6398