Homework 1
Hypothesis testing
Directions
Please write up solutions directly in the document. Be sure to save your document as a PDF with the file name LastName_Homework1.pdf. Provide clear and complete sentences. You may work with others in the class on this assignment, but you must turn in this assignment individually and give responses in your own words.
Due date: Tuesday, October 8th at 11:59pm
Questions
Earlier in the course, we examined the fairness of NFL overtimes under the old “sudden death” rules, and we found that it was incredibly unlikely that the result of 240 wins by the coin-flip winning team would happen in 428 games if there was no advantage given to the team that won the coin flip and thus got the ball first. To fix this, the NFL instituted new rules starting in 2011 that aimed to fix this fairness issue. But did the rule changes actually fix the issue?
Since the rule change in 2011, there have been 192 overtime games that did not end in a tie. In those games, the team that won the coin flip and got the ball first won 108 of those games. Based on this new data, do these new rules still give an advantage to the team that wins the coin flip and gets the ball first? Assume that our significance level threshold is 3%.
1. Describe the null hypothesis that we are testing in this scenario.
2. What percentage of the games were won by the coin-flip winning team? Based on this answer relative to your null hypothesis, what is your initial conjecture to the research question?
3. Create a sampler in TinkerPlots that reflects this null hypothesis, and answer the following questions:
a. What did you set “draw” and “repeat” to? Explain.
b. What type of device did you select, and how did you choose the labels? Explain.
c. How does your device reflect the null hypothesis you described?
d. Paste an image of your sampler below:
4. Run one trial of your sampler model, and paste a plot of the results below. What does a single dot in that plot represent?
5. What measure will you collect statistics on and why? How will collecting statistics on this summary measure help you answer the research question?
6. Run 500 trials of the simulation and create a sampling distribution of the statistic of your choice. What does a single dot in this plot represent?
7. Find the p-value for this test, and re-paste an image of your sampling distribution that shows how you found the p-value.
8. Write up a conclusion in the context of the problem that answers the research question originally posed. Explain how your analysis determined this conclusion.
9. In the original NFL activity that looked at the old overtime rules, we determined that about 56.1% of the teams that won the coin flip ended up winning the game, which was pretty similar to the percentage found with this new data. In the activity from class, we found a p-value around 1%. Why is this p-value so different despite the raw winning percentages being so similar? Explain.
Karen took a multiple choice test with 50 questions on it, with each question has 4 choices. Karen’s result was 16 correct questions out of the 50 total. Do you think that Karen actually studied for this test, or was Karen just randomly guessing answers to the questions? Assume that our significance level threshold is 7%.
10. Describe the null hypothesis that we are testing in this scenario.
11. What percent of the questions did Karen get correct? Based on this answer relative to your null hypothesis, what is your initial conjecture to the research question?
12. Create a sampler in TinkerPlots that reflects this null hypothesis, and answer the following questions:
a. What did you set “draw” and “repeat” to? Explain.
b. What type of device did you select, and how did you choose the labels? Explain.
c. How does your device reflect the null hypothesis you described?
d. Paste an image of your sampler below:
13. Run one trial of your sampler model, and paste a plot of the results below. What does a single dot in that plot represent?
14. What measure will you collect statistics on and why? How will collecting statistics on this summary measure help you answer the research question?
15. Run 500 trials of the simulation and create a sampling distribution of the statistic of your choice. What does a single dot in this plot represent?
16. Find the p-value for this test, and re-paste an image of your sampling distribution that shows how you found the p-value.
17. Interpret what this p-value means in the context of the problem. (Use this format: There is a __% chance that [something happens], assuming that [something] is true.)
18. Write up a conclusion in the context of the problem that answers the research question originally posed. Explain how your analysis determined this conclusion.