Part I - Hypothesis testing and statistical reasoning
At this point in the quarter, you have been introduced to many statistical hypothesis-testing procedures. While they are different computationally, there is a common logic and reasoning underlying hypothesis testing, which is that when deciding between the null and alternative hypotheses, tentatively assume the null to be true, and determine the long-run probability of obtaining results in the sample data resembling your results (over the course of many, many replications of your research study). If this probability is equal to or lower than a low-probability cutpoint (usually .05), then reject the null hypothesis as it is unlikely to be correct, and favor the alternative hypothesis. If this probability is higher than the low-probability cutpoint, retain the null hypothesis.
The scenario described below effectively translates into a test of a hypothesis about a sample proportion. The most difficult part of the questions that follow is not conducting the test of the hypotheses itself, but translating the events described in the scenario below into the correct null/alternative hypothesis statements. Once you have done that, the statistical test is pretty basic. The correct statistical test was covered early in the first half of SOC 113. Read the scenario described below and answer the questions that follow:
Part II - Simple linear regression applications
1) On the course website, there is a data file (FINAL_Q2) containing monthly measurements of temperature (measured in degrees Fahrenheit) and monthly precipitation (measured as inches of rainfall) in three different US cities: Los Angeles, Chicago, and New York City. You will conduct three simple linear regressions in which you test the association between temperature (the EV) and precipitation (the RV) in each of the three cities.
a. Run the simple linear regression testing the association between temperature in Los Angeles and precipitation in Los Angeles. Paste the output below:
b. Interpret the value of the slope measuring the association between temperature and precipitation in Los Angeles, and comment on the direction of the association and whether it is statistically significant.
c. During which season does LA get most of its rainfall, or does rainfall appear to be about the same every month, regardless of temperature? Base your answer to this question on the value of the slope and whether it is statistically significant-not the fact that you live here.
d. Run the simple linear regression testing the association between temperature in Chicago and precipitation in Chicago. Paste the output below:
e. Interpret the value of the slope measuring the association between temperature and precipitation in Chicago, and comment on the direction of the association and whether it is statistically significant.
f. During which season does Chicago get most of its rainfall, or does rainfall appear to be about the same every month, regardless of temperature? Base your answer to this question on the value of the slope and whether it is statistically significant.
g. Run the simple linear regression testing the association between temperature in New York City and precipitation in New York City. Paste the output below:
h. Interpret the value of the slope measuring the association between temperature and precipitation in NYC, and comment on the direction of the association and whether it is statistically significant.
i. During which season does NYC get most of its rainfall, or does rainfall appear to be about the same every month, regardless of temperature? Base your answer to this question on the value of the slope and whether it is statistically significant.