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Math 2200Take Home QuizDue Tuesday April 11that the start of classFor each problem: Identify the type of test, write out the null and alternative hypothesis, and include a statement alongwith your decision.1.Marine engines, particularly those oflarge container or cargo ships, are rated to burn fuel based on its viscosity.The most common fuel is known as 6 oil and should have a kinematic viscosity of 15 mm/s2at 100oC. Jonny rana set of 12 samples of 6 oil from a shore tank and calculated themeanviscosity as 14.3 mm/s2with a standarddeviation of1.2mm/s2.Can Jonny conclude at 99% confidence that the shore tank of 6 oilisoff spec? Assumethe distribution is approximately normal.2.Gasoline retailers are mandated by the EPA tohave completely transitioned to selling summer-grade gasoline byJune 1stevery year. To be considered summer-grade, the Reid Vapor Pressure (RVP)of the gasolinecan be nomore than 9psi.Enmarketis under suspicion of selling winter grade gas past theJune 1stdeadline. Aninvestigator pulls30 samples of gas from various Enmarketlocations and the mean RVP is found to be9.49psi.If the standard deviation of the test method is known to be0.75psi, can the investigator conclude that they areselling the wrong grade?3.The rumor among gasoline chemists is thatRussian oil/gas is very low quality andRussianboats are rejectedmore often than others.Asasingle barge of gasoline can be worth$7-10 million dollars,ships arerarelyrejected(assume no more than 15% of the time).Shamgan was bored one day while waiting for the cargo boatto arrive and decided to check the old laboratory records.In the last3years a total of38gasoline shipsoriginated from Russia. Of those,7failedtheir chemical testingand were rejected.At a significance level of95%, can Shamgan safely conclude thatRussian gas is more likely tobe rejected thanothergas?