Dissolved organic compound in lakes. 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 and saved in the WISCLAKES file. The population of Wisconsin lakes has a mean DOC value of 15 grams/m3. 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.
Lake | DOC |
Allequash | 9.6 |
Big Muskellunge | 4.5 |
Brown | 13.2 |
Crampton | 4.1 |
Cranberry Bog | 22.6 |
Crystal | 2.7 |
EastLong | 14.7 |
Helmet | 3.5 |
Hiawatha | 13.6 |
Hummingbird | 19.8 |
Kickapoo | 14.3 |
Little Arbor Vitae | 56.9 |
Mary | 25.1 |
Muskellunge | 18.4 |
Northgate Bog | 2.7 |
Paul | 4.2 |
Peter | 30.2 |
Plum | 10.3 |
Reddington Bog | 17.6 |
Sparkling | 2.4 |
Tenderfoot | 17.3 |
Trout Bog | 38.8 |
Trout Lake | 3.0 |
Ward | 5.8 |
West Long | 7.6 |
Based on Langman, O. C., et al. “Control of dissolved oxygen in northern temperate lakes over scales ranging from minutes to days.” Aquatic Biology , Vol. 9, May 2010.
Conclusions and Consequences for a Test of Hypothesis
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Conclusion | H0 True | Ha True |
Accept H0 (Assume H0 True) Reject H0 (Assume Ha True) | Correct decision Type I error (probability α) | Type II error (probability β) Correct decision |
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