Statistics Project 3 (1)

AQI for Jefferson County in 2022 For the final project in the Intro to Statistics Class, we will be analyzing and comprehending the data collected for the Air Quality Index in the United States for the year 2022. This data is provided by the Environmental Protection Agency published November 14th, 2022. The data is organized by state, the date (either when the data was collected or inputted), county name, defining site (where data was collected), state and county code, AQI number, category (defined as good, moderate, unhealthy, etc.), defining parameters (ex: ozone), and number of sites reporting. The goal of this project is to understand the relationship between Jefferson County’s air quality in Colorado compared to Denver County’s air quality in Colorado. To do this, we will analyze the average AQI. However, it is good to keep in mind that this data does not cover every square foot of these counties, therefore it is impossible to have a complete representation for the entire area, but there are multiple data collection sites to represent the air quality for that specific area. We decided to analyze Jefferson County’s AQI compared to Denver county’s AQI because they are similar in location and population, instead of comparing it to the nation’s average (there would be so much difference it wouldn’t make much significance). Hypothesis testing is a statistical method to make a statistical inference on a probational statement about the population parameters (confidence interval). In simple terms, it is a way to test an idea about sample data. We are using this method in order to conduct a one- sample t-test on the average AQI of Jefferson County to identify if there is a statistically significant difference from Denver County’s average AQI. In other words: Is Jefferson County’s AQI higher (worse) than Denver county’s AQI? The key part is how much higher does the AQI have to be in order to be statistically significant in order to make a point? Our null hypothesis ( 𝐻ℴ ) is 𝜇 = 55.13 meaning that Jefferson County’s AQI is the same as Denver County’s AQI . Our alternate hypothesis ( 𝐻𝑎 ) is 𝜇 > 55.13 meaning that Jefferson County’s AQI is larger than Denver County’s AQI, aka worse than. To determine this, the significance level 𝛼 = 0.05 is used. The p-value is a probability to compare against the 𝛼 to see if there is statistical evidence to reject the null hypothesis. If 𝛼 < 𝑝 − ?𝑎𝑙?𝑒 then we reject the null hypothesis. If 𝛼 > 𝑝 − ?𝑎𝑙?𝑒 then we failed to reject the null hypothesis. In order to answer this we must compute a test statistic. To do this we use this equation to determine the t-score, to find the p-value, to compare to the significance level ( 𝛼 ). The 𝑥 value is Jefferson County’s AQI (62.30403). The 𝜇 value is Denver County’s AQI (55.13879). The ? value is the Standard Deviation from the study (24.9517). The 𝑛 value is the sample size (273).

Just looking at the numbers before doing any calculation, we can see that 62 > 55 , so we can infer that Jefferson County’s AQI is worse than Denver County’s AQI. ? = (𝜒−𝜇) 𝑠 √𝑛 ? = (62.304−55.13879) ( 24.9517 √273 ) ? = 4.744734 With this t-score, we then find the approximate p-value that corresponds within the t-table. Our degrees of freedom is 272, which we will round to 200. Following this row, we find that the highest value only goes to 2.60, which is smaller than 4.74434 and select 0.005 in the one-tailed category. (We are following the one tailed section because our alternate hypothesis contains an inequality, it is either true or false). In this case, 0.05 > 0.005 so we reject the null hypothesis. This follows 𝛼 < 𝑝 − ?𝑎𝑙?𝑒 In conclusion, there is significant evidence to support that Jefferson County’s air quality index is greater than 55.13, meaning it is worse than Denver County’s a ir quality index. Using the hypothesis test, we rejected our null hypothesis and used our evidence to support the alternative hypothesis, Ha: 𝜇 > 55.13 . Other questions to think about are whether our air quality is worse due to inversions, weather, pollution, location, population, or other reasons. When comparing Jefferson County to Denver County, Jefferson County covers a larger area location wise, while Denver is smaller but more population dense (U.S. Census Bureau, 2022). Another option would be to compare Jefferson County’s AQI from 2022 to its score from 2021 or other years past to determine if there is a decrease or increase in air quality. Here is a graph comparing the average AQI (computed by Mr. Forland) and five counties in Colorado. As you can see, Jefferson has the highest AQI value in 2022 with these counties. This information is helpful to scientists in determining air quality patterns, and is also useful for civilians to understand the quality of the air that they breathe. There could be many reasons why Jefferson County’s AQI is much higher, but it is a significant difference, as seen in the graph and with the hypothesis test conclusion.