Editing Statistics and Statistical Programming (Winter 2021)/Problem set 5 (section)

== Statistical Questions ==

===SQ1. Interpret bivariate analyses===

Return to the dataset you imported and worked with in the programming challenges above. Imagine that it comes from a year-long study of bicyclists using a combination of survey and ride-tracking data from Seattle JUMP bikeshare users conducted a few years ago (let's say 2018, just to pick a year). Each row in the data corresponds to a single cyclist/member and the variables correspond to the following measures: 
* <code>x</code>: Average daily distance cycled (in miles) measured via bicycle dock check-in/check-out data.   
* <code>j</code>: An indicator (True/False) of whether any rides were recorded between January and March.
* <code>l</code>: An indicator (True/False) of whether the cyclist also uses vehicle rideshare provided by Uber (the company that owns JUMP).
* <code>k</code>: A measure of how frequently the cyclist rode in bad weather, with bad weather defined using a standard measure provided by the U.S. NOAA (National Oceanic and Atmospheric Administration) and the categories (none, some, a lot, all) defined in terms of empirical quartiles within the dataset.
* <code>y</code>: A continuous measure of income calculated in tens of thousands of dollars and scaled so that "0" = average income for a JUMP user (i.e., a value of "5" = $50,000 more per year than an average JUMP user).

# Return to the conditional means you created in PC6 above. Given the information you now have about the study, how would you interpret them? Does there seem to be any sort of relationship between the two variables?
# Return to the bivariate contingency table you created in PC7 above. Given the information you now have about the study, how would you interpret it? Does there seem to be any sort of relationship between the two variables?
# Return to the scatterplot you created in PC8 above. Given the information you now have about the study, how would you interpret it? Does there seem to be any sort of relationship between the two variables?

===SQ2. Birthdays revisited (Optional bonus!)===

'''Optional bonus statistical question'''

You did a question about birthdays in the context of one of the textbook exercises for ''OpenIntro'' Chapter 3. Here's an opportunity to apply your knowledge and extend that exercise. Note that you can absolutely use R to help calculate the solutions to both parts of this problem. That said, it's a super famous problem and answers/examples are all over the internet, so if you want to challenge yourself, don't look at them while you're working on it! The only hint I'll give you is that you may find [https://en.wikipedia.org/wiki/Binomial_coefficient binomial coefficients] useful and the <code>choose()</code>) function can calculate them for you in R.

# Imagine that there were 25 people in this class and that I offered you a choice between two bets: Bet #1 is determined by the flip of a fair coin. You can choose heads or tails and you win the bet if your choice turns out to be correct). Bet #2 is determined by whether any two members of that previous version of the class shared a birthday. If a birthday was shared I win the bet, and if no shared birthdays were shared you win the bet. Assuming you want the best chance of winning, which bet should you choose?
# Now calculate the probability that any two members of our 5 person class share a birthday and compare this probability with the results of SQ2.1 above.