European scientists sampled rivers in various seasons for chemical composition and algae growth (http://archive.ics.uci. edu/ml/datasets/Coil+1999+Competition+Data). The following is a random sample of 15 measurements from high-flow rivers and 13 from low-flow rivers of a total algae content (units are mg/L).

(a) Test the null hypothesis at α = 0.05, that the amount of algae content is the same in both high- and low-flow rivers. Is the alternative one or two sided?

(b) Find a 95% confidence interval for the difference in the mean algae content for the two flow rates.

(c) Is the value zero contained in the 95% confidence interval? Explain the connection with the conclusion you reached in part (a).

(d) Do box plots of algae content by flow rate show any violations of the assumptions for the tests and confidence interval that you performed?

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High Low High Low 18.4 31.0 43.1 23.3 23.4 26.0 23.8 59.6 49.5 41.8 33.6 35.8 65.0 38.7 47.3 41.5 75.8 11.8 56.0 34.1 43.9 16.4 78.8 33.3 48.9 17.8 55.0 56.4