this is homework excel page attached
For the activities of Module 7 please work in the Mod 7 tab you have created.
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. If phat is the proportion of days with AQI above 50, then we need to have both n*phat and n*(1-phat) greater than or equal to 10.
- 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 city our county near where you live and then check these conditions again.
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 7.1 from our text. Confirm your results using StatCrunch, inserting your StatCrunch results into your worksheet.
We are 95% confident that the actual proportion of days with AQI that is not “Good” is within the confidence interval we found here.
Now find the 90% confidence interval using any method (by hand or with StatCrunch). How is the 90% confidence interval different than the 95% confidence interval? Why is this so?
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