you are an analyst working for the new Joint High Speed Vessel(JHSV) program office. Several tests have been conducted on twodifferent types of experimental test vessels (denoted simply “1”and “2”) to determine their performance characteristics undervarious loading and sea state conditions.

With detailed data on the fuel consumption of vessel \"1,\" andwith the Navy's new focus on energy efficiency, the program managerwants to test whether the vessel beats the design specs in terms ofmean hourly fuel consumption. You decide to conduct a large samplehypothesis test of the data with the goal of conclusivelydemonstrating, if possible, that the data support the claim thatthe mean hourly fuel consumption is less than 50 gph (gallons perhour) at 35 knots. Given that for 36 (independent) hours ofoperation at 35 kts you observe y-bar 49.5 gph with s=2 gph, andusing a significance level of a=0.05:

a. Write out the null and alternative hypotheses.

b. Calculate the test statistic.

c. Calculate and state the rejection region or p-value.

d. Conduct the test and state the outcome. State the outcomeboth in terms of accepting or rejecting the null hypothesis andthen in terms of what the result means in the context of thisparticular problem.