Data 2.4 on page 68 introduces the dataset FloridaLakes and discusses the correlation between the acidity (pH) for a sample of n = 53 Florida lakes and the average mercury level (ppm) found in fish taken from each lake. We saw in Chapter 2 that there appears to be a negative trend in the scatterplot between the two variables. We wish to test whether there is significant evidence of a negative correlation between pH and mercury levels. A randomization distribution based on the data is shown in Figure B.11. The sample statistic of interest is the sample correlation.
(a) What are the null and alternative hypotheses?

(b) Use Figure B.11 to give a very rough estimate of the sample correlation corresponding to a p-value of 0.30. Explain your reasoning.

(c) Use Figure B.11 to give a very rough estimate of the sample correlation corresponding to a p-value of 0.01. Explain your reasoning.

Figure B.11

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.

Transcribed Image Text:

400 300 200 100 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 Correlation Frequency