We Helped With This R Studio Programming Homework: Have A Similar One?

Worksheet 3 - Data Analysis (100 points)

This worksheet is designed to help you practice using R to organize, analyze, and present data.

Reminder: Follow the correct formatting for all worksheets and assignments (12 pt font, double-spaced, do not include original questions). Incorrect formatting will result in a 5% penalty on this assignment.

Answer/address all of the following questions. In all cases, we require that your work be typed and that you copy your summary tables and graphs onto your answer document.

Please note for all questions:

* TABLES must have (i) a proper caption above and (ii) a heading for each column indicating what data are in the column and the unit of measure (e.g. cm, grams, %).

*  GRAPHS must have (i) a proper caption below, (ii) a title for each axis indicating what data are being shown and the unit of measure (e.g. cm, grams, %), and (iii) if needed, means plotted with standard deviations shown as error bars. For graphs showing relationships between two variables, choose a dependent variable (i.e., species composition or biomass) that will be shown on the Y-axis and an independent variable (e.g. distance from the shore, water depth, soil depth, etc.) which will be shown on the X-axis.

Case Study 1 (39 points)

Hennington pond was the only pond on the FIU campus not treated with chemicals or subjected to storm run-off. In March 2007, a sewage main ruptured and the lake became contaminated with sewage effluent.

You have been provided with data on the phosphorus levels (ug/L) in Hennington pond for two years: 2004 (before perturbation) and 2007 (after perturbation). For both years, sampling was conducted by collecting water samples from 20 random sites within the pond.

Based on observations of Hennington pond during 2004 and 2007, we could ask the following question:

Has the Phosphorus level in Hennington pond changed between 2004 and 2007?

1. For the study above, identify the following: (4 points)
1. Population
2. Sample
3. Parameter
4. Statistics
2. For the study above, identify the following: (3 points)
1. Dependent Variable
2. Independent Variable
3. Is the independent variable categorical or numerical?
3. Write a null, two-tailed alternative, and one-tailed alternative statistical hypothesis for this study. (3 Points)
4. Using data given, produce a summary table (do NOT include raw data) showing the mean phosphorus level and standard deviations in 2004 and 2007. Make sure you include a table caption above it and all necessary labels for clarification. (5 points)
5. Produce a bar graph that shows the mean phosphorus levels in 2004 and 2007. Remember to include axes titles and error bars, as well as a figure caption below the graph. (5 points)
6. Describe the results of the bar graph above. Remember that results are about patterns/trends. You do not simply restate numbers. (2 points)
7. What is the purpose of α (level of significance) in statistics? What would you set you α value at? (2 points)
8. Explain why you would use a t-test to analyze this data. (2 points)
9. Analyze your data using a t-test and place the output below. (5 points)
10. For your two-tailed P-value: (3 points)
1. Is your P-value greater than, less than, or equal to your α value?
2. Do you reject or fail to reject the null hypothesis?
3. Write out the appropriate conclusion (either the null or alternative hypothesis).
11. For your one-tailed P-value: (3 points)
1. Is your P-value greater than, less than, or equal to your α value?
2. Do you reject or fail to reject the null hypothesis?
3. Write out the appropriate conclusion (either the null or alternative hypothesis).
12. Can you prove without a doubt that the sewage main rupture is the cause of a change in phosphorus levels? (2 points)

Case Study 2 (33 points)

On the FIU campus there are three large freshwater ponds: DM pond, OE pond, and Hennington pond. The FIU irrigation committee has decided to increase the drainage of water to one of the three ponds to reduce flooding on campus. Therefore, they are interested in knowing which pond(s) could withstand receiving more water without overflowing.

You have been provided with data on the water depth (meters) in the three ponds. For each pond, sampling was conducted by measuring the water depth at 20 random points within each pond.

Based on observations of these three ponds and the need to increase water flow into one of the ponds, we could put forth the following questions:

Is there a significant difference in average yearly water levels across the three ponds?

13. For the study above, identify the following: (4 points)
1. Population
2. Sample
3. Parameter
4. Statistics
14. For the study above, identify the following: (3 points)
1. Dependent Variable
2. Independent Variable
3. Is the independent variable categorical or numerical?
15. Write a null and alternative statistical hypothesis for this study. Be careful with your alternative hypothesis! (3 Points)
16. Using data given, produce a summary table (do NOT include raw data) showing the mean water level and standard deviations in each of the three ponds. Make sure you include a table caption all necessary labels for clarification. (6 points)
17. Produce a bar graph that shows the mean water levels for all three ponds. Remember to include axes titles and error bars, as well as a figure caption below the graph. (5 points)
18. Describe the results of the bar graph above. Remember that results are about patterns/trends. You do not simply restate numbers. (2 points)
19. For this study, why are you using an ANOVA instead of a t-test? (2 points)
20. Analyze your data using an ANOVA and place the output below. (5 points)
21. For your P-value: (3 points)
1. Is your P-value greater than, less than, or equal to your α value?
2. Do you reject or fail to reject the null hypothesis?
3. Write out the appropriate conclusion (either the null or alternative hypothesis).

Case Study 3 (28 points)

You have been provided with data on the percentage cover and average height of Thalassia testudinum (Turtlegrass, which is an aquatic plant that lives in the ocean) along a 50 meter transect running from the shoreline out into the water at Crandon Park beach. Sampling was conducted using the line transect sampling technique.

Based on observations at Crandon Park, we could put forth the following questions:

Does the percentage cover of Thalassia testudinum (Turtlegrass) change with distance from the shore?

22. For the study above, identify the following: (4 points)

a.       Population

b.       Sample

c.       Parameter

d.       Statistics

23. For the study above, identify the following: (3 points)

e.       Dependent Variable

f.        Independent Variable

g.       Is the independent variable categorical or numerical?

24. Write a null and alternative statistical hypothesis for this study. Remember the wording specific to regression analysis!  (2 Points)

25. Produce a scatter plot which show the change in percentage cover of Thalassia testudinum with distance from shore / distance along the transect. Remember to include a linear trend line. Be careful to put the independent and dependent variables on the correct axes. Remember to include a figure caption below the graph.  (7 points)

26. Explain in words what the equation of the regression line from the previous question means. Make sure you relate it to the graphs and discuss both the slope and y-intercept (Hint: What happens if you are at the shoreline? What happens as your move away from the shore and out to sea?) (2 points)

27. Explain what the R² value on the graph tells you about the data fit and the strength of the linear relationship between this study’s variables. (2 points)

28. Analyze your data with a linear regression for the relationships between distance from the transect and percentage cover of Thalassia testudinum. Place the output below. (5 points)

29. For your P-value: (3 points)

4. Is your P-value greater than, less than, or equal to your α value?
5. Do you reject or fail to reject the null hypothesis?
6. Write out the appropriate conclusion (either the null or alternative hypothesis).