美国大学统计学作业关于假设检验
1) A tire company claims that itsradial tires give a better a gas mileage than its standard tires. To evaluate this claim, twelve cars wereselected and equipped with the radial tires, and driven over a test course, andthe cars’ gas economy was measured. Thenthe same cars were equipped with regular tires and driven by the same driversover the same test course. The gaseconomy was measured. The data are givenbelow. Can the company make thisclaim? Use α = .05.
H null: μd=0
H alternative:μd≠0
数据看下面的表格
从这里可以得到test statistic=1.33,然后找到t table.
在degrees of freedom=11时，1.33处于1.088和1.363之间
但是因为我们的hypothesis test是two-tailed的，所以得到的p-value要乘以2
即0.2≤p-value≤0.3
因为α=0.05小<0.2<p-value.
∴Don't reject H null.
因为不能拒绝H null,所以μd有可能为0.也就是说
“itsradial tires give a better a gas mileage than its standard tires.”这句话不一定是对的.
Conclusion:the company cannot make this claim.