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The backbone of statistics is probability. In this assignment, we will focus on
The backbone of statistics is probability. In this assignment, we will focus on the frequentist version of probability (your textbook talks about Bayesian as well). To practice working with probabilities, we will use a simulated dataset measuring whether crime occurred in cities (0 = no; 1 = yes) and whether the cities had greening efforts (community maintenance efforts) or not (0 = no; 1 = yes). Both of these variables are binary variables, which means there are two discrete categories. Also, remember, probability can be thought of as a percentage chance of some event occurring (e.g., 50% chance of rain). As such, probabilities must be between 0 and 1.
Part 1.
a. What is the probability of a crime occuring in a city WITHOUT taking into account whether the lot was greened? Hint: P(Crime) = total crime / total # of observations
b. What is the probability that a lot was greened WITHOUT taking into account whether there was crime or not? Hint: P(Greening) = total greening / total # of observations
Note: Remember, the probability in this case is just the proportion for each variable! Calculate these using Jamovi.
Part 2.
a. Using Jamovi, create a table of the data, with crime as the columns and greening as the rows. Copy and paste the final table here.
b. What are the percentages for each combination in the table?
Part 3. (Hint: You will use Jamovi but you might need to do a quick calculation using a calculator on your device to arrive at the final answer like how we did in class on 9/17):
a. Find the joint probability of both crime and greening efforts occuring. Hint: you can find the joint probabilities by finding the count where Crime = 1 and Maintenance = 1 in the contingency table and dividing by the total number of observations.
b. Find the conditional probability of crime occurring (Crime = 1) given that maintenance did not occur (Maintenance = 0).
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