The Department of Weights and Measures in a Southern State

question 46

Essay

The Department of Weights and Measures in a southern state has the responsibility for making sure that all commercial weighing and measuring devices are working properly.For example,when a gasoline pump indicates that 1 gallon has been pumped,it is expected that 1 gallon of gasoline will actually have been pumped.The problem is that there is variation in the filling process.The state's standards call for the mean amount of gasoline to be 1.0 gallon with a standard deviation not to exceed 0.010 gallons.Recently,the department came to a gasoline station and filled 10 cans until the pump read 1.0 gallon.It then measured precisely the amount of gasoline in each can.The following data were recorded:
Based on these data,what should the Department of Weights and Measures conclude if it wishes to test whether the standard deviation exceeds 0.010 gallons or not,using a 0.05 level of significance?

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Definitions:

Abyssal Plain

Extensive, flat, underwater landscape at the deep ocean floor, usually found at depths between 3,000 and 6,000 meters.

Seafloor Spreading

The process by which new oceanic crust is created at mid-ocean ridges, pushing older crust away from the ridge axis and contributing to continental drift.

Rifting

the process by which the Earth's crust breaks apart, often leading to the formation of new ocean basins.

Red Sea

A narrow sea between the northeastern African continent and the Arabian Peninsula, known for its extensive coral reefs and intense blue waters.