**In this problem, you will analyze the Stat 100 survey 3 data in Fall 2015. The csv file can be downloaded here.. The column variables are described on this webpage. The purpose of this exercise is to find out if there is any association between happiness (a person's subjective well-being) and a person's temperament (introvert/extrovert/ambirvert).**
###a. (2 points)
**Create box plots of `happiness` for the introverts, extroverts and ambiverts. Add the group means to the box plots.**
Show your plots here
###b. (3 points)
**Perform an F-test to determine if there are any significant differences on the reported scale of happiness among introverts, extroverts and ambiverts. (2 pts)**
Show your calculation here
**Report the p-value and state your conclusion. (1 point)**
Write your answer here
###c. (4 points)
**Perform pairwise t-tests with Bonferroni correction to adjust the p-values. (2 pts)**
Show your calculation here
**Determine from the adjusted p-values which pairs of groups show significant differences at the 5% level. (2 pts)**
Write your answer here
###d. (5 points)
**Perform a randomization test by scrambling the `happiness` variable and calculate the values of R2 of the scrambled data. Repeat the experiment at least 5000 times. (3 pts)**
**Note: The result of your randomization test must be *reproducible*. Therefore, you must set a seed number before calling any function involving random numbers. Use `set.seed(your UIN number)`. You can simply follow the procedure in this week's notes. You are not required to optimize the code.**
Show your code here
**Make a histogram of these R = $\sqrt{R^2}$ and indicate the position of the original R (from the unscrambled data). (2 pt)**
Show your plot here
###e. (3 points)
**Use the result of (d) to estimate the p-value. How does this estimated p-value compare to the one computed in part (b)?**
Show your calculation here