The dataset FloridaLakes is introduced in Data 2.4 on page 68, and we return to the dataset in Exercise B.45 on page 315. To see if there is evidence of a negative correlation between pH in lakes and mercury levels in fish, the hypotheses are H₀: ρ = 0 vs H_a: ρ < 0. For the observed sample, with n = 53, we have r = −0.575.

(a) What assumption do we make in creating the randomization distribution?

(b) Where will the randomization distribution be centered?

(c) Describe how you could use index cards to create one simulated sample. How many cards do you need? What will you put on them? What will you do with them? Once you have used the cards to create a simulated sample, what statistic will you calculate from it to use in a randomization distribution? (You don’t have to actually create a simulated sample, just give a description of the process you would follow.)  

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.