## Problem 1

In 25 words or less, what does a p-value represent? *Be careful!!!!*

## Problem 2

Write your own Monte Carlo statistical analysis to test the hypothesis that foot size is correlated with stature (height). Use this fake data set on foot size in Americans.

A. Use ggplot2 to create a scatter plot with height on the x-axis and foot length on the y-axis, and add a line showing the relationship between the variables. Make sure your plot has an informative title and make sure it looks good!

B. Do the analysis:

- Your test statistic is the absolute value of the correlation coefficient (we will discuss this in more detail next week). To calculate the correlation coefficient of two vectors
`x`

and `y`

, you would use the `cor()`

function like this `cor(x,y)`

. You can calculate the absolute value of this number with `abs()`

.
- For each iteration, shuffle the foot length values randomly, and calculate the test statistic for the shuffled foot lengths and the original height variable.
- Repeat this 10,000 times, storing the test statistic each time in a vector called
`cors`

.

C. Make a histogram of `cors`

to get a visual sense of the values. Make sure you have meaningful axis labels, a title, and that the plot looks good!

D. Calculate the value of the test statistic for the original (unshuffled) data, and save to a variable called `original.cor`

E. Calculate the proportion of the elements in `cors`

that are greater than or equal to `original.cor`

F. Write a couple of sentences interpreting these results in terms of the relationship between the two variables and in terms of the null hypothesis. *Be specific!*