NO.PZ2015120604000118
问题如下:
Deli Bur is a high school. A recent survey of 25 student of the high school indicates that the mean time they spend going to school is 40 minutes . This sample's standard deviation is 8 minutes. The distribution of the population is supposed to be normal. The 99% confidence interval for the mean time that all Deli Bur students spend going to the school is:
选项:
A.30.72 to 34.55
B.38.52 to 54.48
C.35.52 to 44.48
解释:
C is correct.
Because the simple size is less than 30, so the confidence interval for the population whose variance is unknow is :
.
To calculate critical value: and df = 24 is 2.797.
So, the confidence interval is 40 ± 2.797(8 / 5) = 40 ± 4.48 = 35.52 to 44.48
本题由于样本数量小于30,且总体方差未知。
可知均值X bar=40,对应的X bar的标准差(即标准误)=8/√25=1.6。
而critical value需要查表求得,如果是正态分布,这个值就是2.58。但这道题对应的是t分布,需要查的是t表(总体方差未知用t)。
本题α=1%,则α/2=0.005。t分布需要考虑自由度,df=n-1=24。通过对应单尾概率0.005和自由度24查表可得t critical value=2.797.
代入公式40±2.797×1.6即可得到答案C选项。
求标准误的时候是用总体的方差除以根号下样本容量。
但本题说:This sample's standard deviation is 8 minutes。这句话难道不是说明标准误为8吗?怎么还要用样本的方差去除以根号下样本容量呢?公式都对不上号啊。