In: Statistics and Probability
The following data was collected from a random sample of Metropolis citizens:
Most Hated Villain | ||||||
Joker | Catwoman | Doomsday | Lex Luthor | Other | ||
Wonder Woman | 22 | 36 | 25 | 20 | 26 | |
Favorite | Superman | 13 | 15 | 34 | 35 | 21 |
Hero | Batman | 33 | 36 | 15 | 15 | 25 |
Other | 16 | 14 | 12 | 20 | 20 |
Using a 'Test for Independence', decide at the 5% significance level if there is sufficient evidence of there being an association between 'Favorite Hero' and 'Most Hated Villain'. Be sure to show all steps to your hypothesis test including: the 2 hypotheses, verifying conditions, test statistic, p-value (or rejection region), and your conclusion in context. While you may put all that in the essay box answer here, this would be a good problem to write out and submit your solution via email. Note that you can use formula to calculate the test statistic, but using a calculator shortcut is just fine (and will save you time).
Conclusion:
There is sufficient evidence to conclude that there being being an association between 'Favorite Hero' and 'Most Hated Villain'