假设检验(t-test)

题目：

The mean emission of all engines of a new design needs to below 20 ppm if the design is to meet new emission requirements.Ten engines are manufactured for testing purposes,and the emission level of each is determined.The emission data is
15.6 16.2 22.5 20.5 16.4 19.4 16.6 17.9 12.7 13.9
Dose the data supply sufficient evidence to conclude that this type of engine meets the new standard?Assume we are willing to risk a Type 1 erroe with probability=0.01

H0:μ=20ppm
Hl:μ<20ppm

x¯=17.17s=2.98

t=17.17−202.9810√=−3.00

Reject H0 if P(x¯=17.17|H0true)<1%

因为n=10，因此去t-table中查看df=9，α=0.01的值，

为2.821,根据对称性知，左侧的t值即为-2.821

而-3<-2.821,

因此，拒绝假设，

即Hl成立