# The Data Set “nail-polish.csv”

Learning Goal: I’m working on a statistics question and need support to help me learn.

Create a clean (no unnecessary output) and well-formatted RMarkdown file that answers the two problems below (note both problems contains multiple parts). Use the #, ## and ### features to separate parts of the document to ease in reading.

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#### PROBLEM 1 (20PTS)

Description: A student, preparing for a triathlon, suspected that the 45 minutes each day she spent training in a chlorinated pool was damaging her nail polish. She wished to investigate whether the color of the nail polish might make a difference. She mounted acrylic nails on sticks and polished them with two different color nail polishes. She soaked them together in a chlorine solution equivalent to a swimming pool’s chlorination and then tapped them 100 times on a computer keyboard to simulate daily stress. She then recorded the % of nail chipped off as measured by scanning images of the nails and using an image processing program. She wishes to find out if the % of nail polish chipped off vary between the two different colors she uses.

The data set “nail-polish.csv” can be accessed using the following line of code:

``df1 <- read.csv("https://raw.githubusercontent.com/hellomissingdata/STA363/main/nail-polish.csv")``

Part 1
Comment on the design of the experiment. Specifically state all the design elements in the context of the problem: the experimental units, the response variable(s), the factor, factor levels, and the treatments. If you were her, what would you do in the experiment to control for nuisance variation or confounding variables?

Part 2
Build an appropriate plot for the design of data. Comment on what you see, including comments on the average and variation in the response. Make sure your plot is properly labeled and would be understandable to an outside viewer (that is, the labels and titles explain the context).

Part 3
Perform the appropriate statistical analysis for this design. State the conclusion of the analysis results of the experiment outcomes, in context.

Part 4
What are the assumptions of the statistical method chosen in part 3? Please perform a residual analysis to check for these assumptions. In your analysis, please provide your graphs and your comments about the model assumptions based on your findings from these graphs.

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