Part 2. Two-sample t-tests

A research group is investigating phytoremediation, which involves the use of plants to clean-up pollutants from the environment. Some species of plants have an ability to tolerate and accumulate heavy metals in their tissues, which consequently removes the pollutants from the environment. One toxin of major concern is arsenic due it is toxicity at very low concentrations and the fact that it does not biodegrade.

This research group claims that a newly developed variety of willow accumulates higher levels of arsenic (measured as mg of arsenic per kg of plant dry weight) than a local species of poplar that is currently used in phytoremediation efforts. The research group conducts an experiment using 21 randomly selected trees from each species that are growing in arsenic contaminated soils. At the end of the experiment, the amount of arsenic (mg/kg) in each tree was measured. Below are the data; assume the data are normally distributed.

Measurements taken from the willow trees:

57.848, 54.176, 54.555, 55.366, 55.903, 56.582, 57.355, 54.426, 55.850, 53.640, 55.385, 55.739, 55.155, 56.428, 55.703, 56.497, 56.035, 53.008, 54.214, 55.200, 58.103

Measurements taken from the poplar trees:

54.604, 54.533, 54.931, 54.612, 54.427, 56.033, 53.895, 54.476, 54.378, 54.404, 56.039, 56.168, 55.215, 53.510, 53.945, 53.184, 55.091, 54.288, 56.052, 54.507, 55.314

(2a) Find the variance of the levels of arsenic accumulated in the willow and poplar trees. Round your answer to three decimal places. (2 points)

(2b) Write the null and alternative hypotheses for a test of variance equality between willow and poplar, and state whether this is a right-, left-, or two-tailed test. (3 points)

(2c) Conduct a test of variance equality using var.test() in R/RStudio. Paste your code and output below. (4 points)

(2d) Using alpha = 0.05, state the statistical decision and interpretation for the test of variance equality. (4 points)

(2e) Given your result in (2d), conduct the appropriate two-sample t-test to test the claim from the research group that a newly developed variety of willow accumulates higher levels of arsenic than a local species of poplar that is currently used in phytoremediation efforts. Paste your code and output below (4 points)

(2f) Using alpha = 0.05 and alpha = 0.01, state the statistical decision and interpretation for your two-sample t-test from (2e). (8 points)