The level of dissolved oxygen in the surface water of a lake is vital to maintaining the lake’s ecosystem. Environmentalists from the University of Wisconsin monitored the dissolved oxygen levels over time for a sample of 25 lakes in the state (Aquatic Biology, May 2010). To ensure a representative sample, the environmentalists focused on several lake characteristics, including dissolved organic compound (DOC). The DOC data (measured in grams per cubic-meters) for the 25 lakes are listed in the accompanying table. The population of Wisconsin lakes has a mean DOC value of 15 grams/m³.
a. Use a hypothesis test (at α = .10) to make an inference about whether the sample is representative of all Wisconsin lakes for the characteristic, dissolved organic compound.
b. What is the likelihood that the test, part a, will detect a mean that differs from 15 grams/m³ if, in fact, μ_a = 14 grams/m³?

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WISCLAKES LAKE DOC LAKE DOC Allequash 9.6 Muskellunge 18.4 Big Muskellunge 4.5 Northgate Bog 2.7 Brown 13.2 Paul 4.2 Crampton 4.1 Peter 30.2 Cranberry Bog 22.6 Plum 10.3 Crystal 2.7 Reddington Bog 17.6 EastLong 14.7 Sparkling 2.4 Helmet 3.5 Tenderfoot 17.3 Hiawatha 13.6 Trout Bog 38.8 Hummingbird 19.8 Trout Lake 3.0 Kickapoo 14.3 Ward 5.8 Little Arbor Vitae 56.9 West Long 7.6 Mary 25.1