Use Excel’s COUNTIF function to find the number of days with a PM2.5 AQI value over 50. On such days, the air quality conditions are considered not to be “Good” per the EPA’s Air Quality Index. Use this to find the proportion of days for which the air quality was not good in your sample (phat). A success will be a day in which the PM2.5 AQI is above 50.
We first must check that the conditions of the Central Limit Theorem apply for estimating proportions in a population.
- The Random and Independent condition is met by the EPA’s collection agencies.
- The Large Sample condition must be checked (by you). If phat is the proportion of days with AQI above 50, then both n*phat and n*(1-phat) must be greater than or equal to 10 to meet the Large Sample condition. Within your Excel file, clearly label and show this condition is met.
- The Big Population condition is met for our data.
When these three conditions are met, we can use the Normal distribution to find probabilities concerning the sample proportion. If your data set does not meet the Large Sample condition, obtain a new data set for a different county that has not already been selected by a classmate. You will then need to check the three conditions of the Central Limit Theorem again, making sure your new data set meets these conditions. Within your Excel file, clearly label and show this condition is met.
Clearly label cells with the names and values for the following: number of successes in sample, sample size, sample proportion of successes, z value multiplier for 95% confidence interval, the estimated standard error, and the confidence interval. By hand calculate the estimated standard error and the confidence interval (using a calculator to do the math) using formulas 7.2 from our text. Confirm your results using StatCrunch, inserting your StatCrunch results into your worksheet in the Excel file. Next, find the 90% confidence interval – by hand or with StatCrunch, and clearly include this information in your Excel file.
Create a single post addressing all of the questions below (using complete and descriptive sentences). Attach your Excel data file (*.xls or *.xlsx) to your discussion post.The Excel file will include not only the data, but also the use of commands and clearly labeled results.
How is the 90% confidence interval you found different than the 95% confidence interval? Why is this so? What concerns might you have regarding the actual proportion of days with AQI that is not “Good”? Without doing any calculations, what might you guess would be the 99% confidence interval for you data? Which confidence interval is likely the most reasonable to consider (90%, 95%, or 99%) and why?