The following is based on information take from Winter Wind Studies in Rocky Mountain National Park, by D. E. Glidden of the Rocky Mountain Nature Association.  At five weather stations on Trail Ridge Road in Rocky Mountain National Park, the peak wind gusts in miles per hour for January and April are recorded below: Weather Station January April 1 139 104 2 122 113 3 126 100 4 64 88 5 78 61 Perform a statistical test with 95% confidence to determine if there is a difference in the peak wind gusts between

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The following is based on information take from Winter Wind Studies in Rocky Mountain National Park, by D. E. Glidden of the Rocky Mountain Nature Association.  At five weather stations on Trail Ridge Road in Rocky Mountain National Park, the peak wind gusts in miles per hour for January and April are recorded below:

Weather
Station
January April
1 139 104
2 122 113
3 126 100
4 64 88
5 78 61

Perform a statistical test with 95% confidence to determine if there is a difference in the peak wind gusts between the two months and supply this information:

 
(a) What is the value of the test statistic?
(b) Find the probability of getting these results if there is no difference between the two months.
(c) What is your conclusion?  Is there evidence of a difference?  Explain.
 
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