Coalbed methane is an important source of natural gas in the United States. The Powder River coalfield has approximately 2500 wells, each producing on average 159,350 cubic feet of gas per day. To...

Coalbed methane is an important source of natural gas in the United States. The Powder River coalfield has approximately 2500 wells, each producing on average 159,350 cubic feet of gas per day. To maintain sufficient storage facilities, the mean well output is carefully monitored. A random sample of 11 wells was obtained, and the daily methane output for each was recorded. The sample mean was x = 163,288 cubic feet and the standard deviation was s = 8792 cubic feet. Assume the distribution of methane output per well per day is normal, and use a = 0.01.

a. Is there any evidence to suggest the mean methane output per well per day has increased?

 b. Find bounds on the p value associated with this hypothesis test.