A study was conducted to examine the association between the average statewide SAT score and the percent of students taking the exam in each state. The hypothesis is that states with more students taking the SAT exam will tend to have lower SAT scores on average. States with a small percentage of students taking the SAT exam are expected to have higher average SAT scores because only the very strong students will be inclined to take the exam. The data are n=50 pairs (xi, yi)=(Percenti, SATi). See below for a scatterplot and computer output for estimated regression and correlation parameters. a. Is there evidence of an association between percent of students taking the SAT and average SAT score? To answer this question, decide which measure of correlation (Pearson or Spearman) is more appropriate and report an estimate of the appropriate correlation and p-value for testing whether the correlation is 0. Provide an interpretation.

b. Interpret the number 1053 in the simple linear regression output.

c. Interpret the number -2.50 in the simple linear regression output.

d. Using the simple linear regression output, estimate the difference in mean SAT score between states with 25% and 75% of students taking the exam.