A At last! The job of your dreams! You are appointed supervisor of garbage collection for the fine city of Richmond. Some of your garbage trucks come back full, some empty. Is there are any connection between whether trucks returned full or empty trucks and whether on the day of collection it was raining? Perhaps people don’t like putting out their garbage in the rain? You have 112 trucks, and when it’s raining, 9 come back full. You count the empty trucks, and when it isn’t raining there are 23 of these. When it is raining, 3 return empty.
a. Write the hypotheses
Ho: there is no association between whether or not it’s raining and garbage truck full or not
Ha: there is....
b. Test at 95%. What are your results? Write up a conclusion in the framework of this question.
Draw a contingency table first...
Use Excel to get the expected values (row total*column total/n)
| 9 | 77 | 86 |
| 3 | 23 | 26 |
| 12 | 100 | 112 |
| 9.214286 | 76.78571 | |
| 2.785714 | 23.21429 | |
| 0.876776 |
Get the p value of 0.876776 using =chitest(...).
The p value is 0.87, which is higher than 0.05 (alpha).
Therefore we fail to reject the null hypothesis. There is no relationship between whether it is raining or not and whether your trucks come back full or empty
c. It’s raining. What is the probability a garbage truck will come back full? Use the proper notation.
Pay attention to the sample space here!
P(Full|Raining) = 9/12
d. You see an empty garbage truck. What is the probability it’s raining? Use the proper notation.
P(Raining|Empty) = 3/26
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