Are metal bands used for tagging harmful to penguins? In Nature, researchers Saraux et al. reported the results of an investigation done to answer this question using a sample of 100 penguins near Antarctica. These penguins had already been tagged with RFID chips, and the researchers randomly assigned 50 of them to receive a metal band on their flippers in addition to the RFID chip. The other 50 penguins did not receive a metal band. The researchers then recorded which penguins were still living 4.5 years into the study. They found results similar to those shown in the table. 

a. Back in Chapter 6 we said that two variables were not associated when the two conditional proportions were the same. In this case, it means the proportion of banded penguins that survived needs to be the same as the proportion of unbanded penguins that survived. Fill in the table provided under the assumption that there is no association between being banding and surviving. 

b. Saying there is no association between banding and penguin survival is the same thing as saying banding and survival are independent. Explain why this is true.

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Survived Died Total Banded Unbanded 50 50 Total 48 52 100