1. Create a variable named "my_feelings" and assign to it your feelings about statistics. ```{r} #### Exercise 1 # Type your code in this shaded section (just below this line) my_feelings <- "Statistics is the best!" # Ok, I did this one for you. ```

2. Use the rflip() command to flip 20 fair coins. Then, use **n**flip() to flip 20 coins. Notice the output is simplified - it only shows the number of heads. Use either rflip() or nflip() to flip 10 unfair coins (in which the probability of heads = 0.80 for each coin). ```{r} #### Exercise 2a # Below this line, type the code to flip 20 fair coins. #### Exercise 2b # Below this line, type the code to flip 20 fair coins using nflip() #### Exercise 2c # Below this line, type the code to flip 10 unfair coins with P(heads = 0.80). ```

3. Use Do() * nflip() to flip 20 fair coins 5 times. Then, flip 10 unfair coins (in which the probability of heads = 0.80 for each coin) 7 times. ```{r} #### Exercise 3a # Below this line, complete the code to flip 20 fair coins 5 times. Do() * nflip() #### Exercise 2b # Below this line, type the code to flip 10 unfair coins with P(heads = 0.80) 7 times. ```

4. Flip 20 fair coins 1,000 times and store the results as **coins**. In other words, assign the results of 1,000 replications of 20 coin flips to the variable **coins**. Then, look at the first several rows of the results using the head() command. ```{r} #### Exercise 4a # Complete the code to flip 20 fair coins 1,000 # times and store the results as coins coins <- Do() * nflip() #### Exercise 4b # Use the head() command to examine the first several rows of results ```

5. The data frame **coins** contains the results of 1,000 replications of 20 coin flips. Construct a histogram of the number of heads in all 1,000 replications. ```{r} #### Exercise 5 # Complete the code to construct your histogram. # Change the XX values in the code below # Don't forget to keep that ~ symbol! # Oh, and notice the variable is called "nflip" histogram(~XX , data=XX) ```

6. Change the colors of the bars and borders in your histogram. Try any colors you'd like. I'd suggest using "lightgreen" and "forestgreen." ```{r} #### Exercise 6 # Add arguments to this command to change the color of your histogram bars and borders # Remember to separate your arguments with commas histogram(~nflip , data=coins, ) ```

7. Change your histogram to have counts represented on the y-axis, bar widths of 1, and a descriptive label on the x-axis. ```{r} #### Exercise 7 # Replace the XX values in the following code to complete the exercise: histogram(~nflip, data=coins, col="XX", border="XX", type="XX", width=XX, xlab = "XX") ```

8. Add a vertical line to your histogram at X = 12. ```{r} #### Exercise 8 # Replace the XX values in the following code to complete the exercise: histogram(~nflip, data=coins, type="count", width=1, xlab = "XX", v = XX) ```

***** ## Tea Time ***** 9. Simulate this experiment with 10,000 replications of coin flips. Then, create a histogram of the results and estimate the p-value from this experiment. ```{r 'tea-time', message=FALSE} # Replace all &&& in the code below to simulate the experiment # Run 10,000 replications and store the results in "tea" tea <- Do(&&&) * nflip(n = &&&, prob = &&&) # Now, plot a histogram of the results # Feel free to change the color of the bars and borders # Replace the &&& to give the x-axis a descriptive name histogram(~nflip, data = tea, col="grey", border="white", width=1, xlab = "&&&") # Estimate the p-value by replacing the &&& prop(~nflip >= &&&, data = tea) ```

10. Explain what this p-value represents. What assumptions were you making when you simulated this experiment? **Answer**: Replace this text with your answer.

***** ## Psychic ***** 11. Simulate this experiment with 10,000 replications. Estimate the p-value. ```{r 'psychic', message=FALSE} # Replace all &&& in the code below to simulate the experiment # Run 10,000 replications and store the results in "psychic" psychic <- Do(&&&) * nflip(n = &&&, prob = &&&) # Now, plot a histogram of the results. # Replace the &&& to give the x-axis a descriptive name # Highlight the results obtained in this study by replacing # the &&& in v=&&& to draw a vertical line histogram(~nflip, data = psychic, col="grey", border="white", width=1, xlab = "&&&", v=&&&) # Estimate the p-value by replacing the &&& prop(~nflip >= &&&, data = psychic) ```

12. Explain what this p-value represents. What assumptions were you making when you simulated this experiment? **Answer**: Replace this text with your answer.

***** ## Hot Hand ***** 13. Simulate this experiment with 10,000 replications. Estimate the p-value. ```{r 'hot-hand-simulation', message=FALSE} # The code has been provided bball <- Do(133) * nflip(n = 1, prob = 0.44) # Calculate the length of each streak and store as "sim_streak" # Don't worry about understanding this code sim_streak <- diff(which(c(0, bball$nflip, 0)==0)) - 1 # Histogram histogram(~sim_streak, width=1, col="lightblue", border="white", type="count", xlab="Streak Length for simulated shooter", ylab="Number of streaks", xlim=c(-1, 7)) ```

14. Compare the streak lengths of the simulated shooter to those of Kobe Bryant. From this comparison, do you have evidence that Kobe had a hot hand? Briefly explain. **Answer**: Replace this text with your answer.

End of Lab Report #1