Are metal bands used for tagging harmful to penguins? Researchers Saraux and colleagues (Nature, 2011) reported the results of a study done to investigate this 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. Researchers found that 16 of the banded penguins were still living 4.5 years into the study compared to 31 of the unbanded penguins that were still living. Are unbanded penguins more likely to be living after 4.5 years than are banded penguins? 

a. State the hypotheses either in words or using appropriate symbols. 

b. Are the validity conditions met here for theory-based methods? Explain. 

c. Determine the standardized statistic and corresponding p-value. 

d. State your conclusion (with appropriate justification based on your p-value and stated significance level) in the context of the research question. Be sure to also address the issues of causation and generalizability.