Figure 4.26 shows a scatterplot of the acidity (pH) for a sample of n = 53 Florida lakes vs the average mercury level (ppm) found in fish taken from each lake. The full dataset is introduced in Data 2.4 on page 68 and is available in FloridaLakes. There appears to be a negative trend in the scatterplot, and we wish to test whether there is significant evidence of a negative association between pH and mercury levels.

Figure 4.26

(a) What are the null and alternative hypotheses?

(b) For these data, a statistical software package produces the following output:

r = ˆ’0.575 p-value = 0.000017

Use the p-value to give the conclusion of the test. Include an assessment of the strength of the evidence and state your result in terms of rejecting or failing to reject H₀ and in terms of pH and mercury.
(c) Is this convincing evidence that low pH causes the average mercury level in fish to increase? Why or why not?

Data 2.4 on page 68

The FloridaLakes dataset describes characteristics of water samples taken at n = 53 Florida lakes. Alkalinity (concentration of calcium carbonate in mg/L) and acidity (pH) are given for each lake. In addition, the average mercury level is recorded for a sample of fish (large mouth bass) from each lake. A standardized mercury level is obtained by adjusting the mercury averages to account for the age of the fish in each sample. Notice that the cases are the 53 lakes and that all four variables are quantitative.

1.4 1.2 1.0 - 0.8 0.6 0.4 0.2 0.0 3 4 5 9. pH AvgMercury Co