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

Category | Programming |
---|---|

Subject | R | R Studio |

Difficulty | Undergraduate |

Status | Solved |

More Info | Probability And Statistics Assignment |

## Short Assignment Requirements

## Assignment Description

__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 axi**s 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?**

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

__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?**

- For the study above, identify the following: (4 points)
- Population
- Sample
- Parameter
- Statistics
- For the study above, identify the following: (3 points)
- Dependent Variable
- Independent Variable
- Is the independent variable categorical or numerical?
- Write a
**null**and**alternative**for this study.__statistical__hypothesis*Be careful with your alternative hypothesis!*(3 Points) - Using data given, produce a summary
table (
) showing the mean water level and standard deviations in each of the three ponds.__do NOT include raw data__*Make sure you include a table caption all necessary labels for clarification.*(6 points) - 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) - Describe the
**results**of the bar graph above. Remember that results are about**patterns/trends**. You do not simply restate numbers. (2 points) - For this study, why are you
using an
**ANOVA**instead of a t-test? (2 points) - Analyze your data using an
**ANOVA**and place the output below. (5 points) - For your
**P-value**: (3 points) - Is your P-value greater than, less than, or equal to your α value?
- Do you reject or fail to reject the null hypothesis?
- 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 **R ^{2 }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)

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