At five weather stations on the Trail Ridge Road in Rocky Mountain National Park, the peak wind gusts (mph) in January as well as April are recorded below. A forest ranger claims that, at the 5% level of significance, there is the significant difference between average peak wind gusts in January and April along this road. Suppose that wind gusts are approximately normally distributed.
Weather Station January April
1 139 109
2 122 113
3 126 100
4 79 84
5 68 68
Describe the null as well as alternative hypotheses and the compute.