We are studying the geology of several areas in the Sierra Nevada of California to understand how they were formed. If they were all formed about the same time we would expect that they would have about the same percentage of carboniferous sand (sand with fossil carbon). We have extracted samples from Joshua Tree National Monument, Sequoia National Forest, Shasta National Forest, Tahoe National Forest, and Yosemite National Park (given in the data below). Read the data into a data frame in R and answer the following questions:

a. Make two boxplots, one with and one without notches. What is the difference between the two plots (i.e.: what do notches tell us that the regular boxplot does not)? Based on your plots, does it appear likely or unlikely that there is a difference between the ages of the parks?

b. Name the parametric test we should use to answer the question. List the null and alternative hypotheses in words (related to the question at hand) and in symbols (if applicable).

c. Run the appropriate built in parametric test in R. Paste the results in your answer sheet.Based on the results, do you reject or fail to reject the null hypothesis? State your reasons why.

d. We are worried that the data may not fit the assumptions to use a parametric test. Name the nonparametric test we should use and list the null and alternative hypotheses in words (related to the question at hand) and in symbols (if applicable).

e. Run the appropriate built in nonparametric test in R. Paste the results in your answer sheet. Based on the results, do you reject or fail to reject the null hypothesis? State your reasons why.

carbon area

19.2 Yosemite

18.7 Yosemite

21.3 Yosemite

16.5 Yosemite

17.3 Yosemite

22.4 Yosemite

18.7 Sequoia

14.3 Sequoia

20.2 Sequoia

17.6 Sequoia

19.3 Sequoia

16.1 Sequoia

12.5 Tahoe

14.3 Tahoe

8.7 Tahoe

11.4 Tahoe

9.5 Tahoe

16.5 Tahoe

20.3 Joshua

22.5 Joshua

17.6 Joshua

18.4 Joshua

15.9 Joshua

19.0 Joshua

19.9 Shasta

25.3 Shasta

17.6 Shasta

20.2 Shasta

18.4 Shasta

19.1 Shasta