11.82 Both surface soil and subsoil specimens were taken from eight randomly selected agricultural locations in a particular county. The soil specimens were analyzed to determine both surface pH and subsoil pH, with the results shown in the accompanying table.

Location 1 2 3 4 5 6 7 8 Surface pH 6.55 5.98 5.59 6.17 5.92 6.18 6.43 5.68 Subsoil pH 6.78 6.14 5.80 5.91 6.10 6.01 6.18 5.88

a. Compute a 90% confidence interval for the mean difference between surface and subsoil pH for agricultural land in this county.

b. What assumptions are necessary for the interval in Part

(a) to be valid?