# How do I figure out which test to use for this following set of data?

## A researcher at the environmental protection agency (EPA) wants to determine if the air quality in the united states has decreased over the past 2 years. The researcher selected a random sample of 10 Metropolitan areas and found the number of days each that failed to meet acceptable air quality standard. The data are shown below year: Year 1 ... 18 125 9 22 138 29 1 19 17 31 Year 2 ... 24 152 13 21 152 23 6 31 34 20 What are the relevant and alternative hypotheses? What is the MOST appropriate analysis for the data? What test do I use? What are the degrees of freedom? What is the conclusion when $\alpha = .10$?

Dec 16, 2017

You would use ANOVA to see if there is any significant difference between the means of the two years.

#### Explanation:

Because it is more convincing to disprove something with a statistical test, set up the null hypothesis to be the thing that you really expect. Then, if your null hypothesis is 'rejected' you are fairly confident that it is NOT true. The alternative should only and always be simply the inverse/reverse of the null! Don't try to add things - those are for other tests.

So, if you think that there IS a change, the null hypothesis should be:
"There is no significant difference between the means of Year1 and Year2."
The alternative hypothesis is thus:
"There is a significant difference between the means of Year1 and Year2."

http://cba.ualr.edu/smartstat/topics/anova/example.pdf

https://statistics.laerd.com/statistical-guides/one-way-anova-statistical-guide.php