Suppose that during the peak growing season random samples of 170 oak trees and 185 chestnut trees in Victoria were investigated where it was found that 13% of oak trees and 8% of chestnut trees had death cap mushrooms growing under them.

Test the claim that the proportion of oak trees with death cap mushrooms growing underneath (p1) is greater than the proportion of chestnut trees with death cap mushrooms growing underneath (p2).

(a) Define the parameter of interest using the correct notation. Then, state the null and alternative hypotheses for this study.

(b) Calculate the observed value of the test statistic. State the distribution (and degrees of freedom if needed) it follows.

(c) Compute the p-value or provide a range of appropriate values for the p-value.

(d) Using the significance level = 0.01, state your conclusions about if the proportion of oak trees with death cap mushrooms underneath is greater than the proportion of chestnut trees with death cap mushrooms underneath.