The article “Statistical Comparison of Heavy Metal Concentrations in Various Louisiana Sediments” (Environmental Monitoring and Assessment [1984]: 163–170) gave the accompanying data on depth (m), zinc concentration (ppm), and iron concentration (%) for 17 core samples.

a. Using a .05 significance level, test appropriate hypotheses to determine whether a correlation exists between depth and zinc concentration.

b. Using a .05 significance level, do the data strongly suggest a correlation between depth and iron concentration?

c. Calculate the slope and intercept of the estimated regression line relating y = iron concentration and x = depth.

d. Use the estimated regression equation to construct a 95% prediction interval for the iron concentration of a single core sample taken at a depth of 50 m.

e. Compute and interpret a 95% interval estimate for the true average iron concentration of core samples taken at 70 m.

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Core Depth 0.2 2.0 5.8 6.5 7.6 122 3 4 5 879 6 9 10 11 12 13 14 15 16 17 12.2 16.4 20.8 22.5 29.0 31.7 38.0 41.5 60.0 61.5 72.0 104.0 Zinc 86 77 91 86 81 87 94 92 90 108 112 101 88 99 90 98 70 Iron 3.4 2.9 3.1 3.4 3.2 2.9 3.2 3.4 3.1 4.0 3.4 3.6 3.7 3.5 3.4 3.5 4.8