题目
A random sample of 8 three-month-old golden retriever dogs is taken. The heights of the golden retrievers are recorded.
Using this sample, a 95% confidence interval for the mean height, in cm, of three-month-old golden retrievers is found to be (45.72, 53.88)
(a) Find a 99% confidence interval for the mean height. You may assume that the heights are normally distributed with known population standard deviation.
Some summary statistics for the weights, x kg, of this sample are given below.
| 91.2 | |
| 1145.16 | |
| n | 8 |
(b) Calculate unbiased estimates of the mean and the variance of the weights of three-month-old golden retrievers.
A further random sample of 24 three-month-old golden retrievers is taken. The unbiased estimates of the mean and the variance of the weights, in kg, from this sample are found to be 10.8 and 17.64 respectively.
(c) Estimate the standard error of the mean weight for the combined sample of 32 three-month-old golden retrievers.
题目中文翻译
抽取了 8 只三个月大的金毛寻回犬作为随机样本。 记录了这些金毛寻回犬的身高。
利用这个样本，求得三个月大金毛寻回犬平均身高（单位 cm）的 95% 置信区间为 (45.72, 53.88)。
(a) 求平均身高的 99% 置信区间。 你可以假设身高服从正态分布且总体标准差已知。
下列给出了该样本体重 x kg 的一些统计量。
| 91.2 | |
| 1145.16 | |
| n | 8 |
(b) 求三个月大金毛寻回犬体重的均值和方差的无偏估计。
又抽取了另外 24 只三个月大的金毛寻回犬。 该样本中体重（单位 kg）的均值和方差的无偏估计分别为 10.8 和 17.64。
(c) 估计 32 只三个月大金毛寻回犬合并样本中体重均值的标准误。