4) A recent article (Hauser, Glynn, and Wood, 2007) described a study that investigated whether rhesus monkeys have some ability to understand gestures made by humans. In one part of the study, the experimenter approached individual rhesus monkeys and placed two boxes an equal distance from the monkey. The experimenter then placed food in one of the boxes, making sure that the monkey could tell that one of the boxes received food without revealing which one. Finally, the researcher made eye contact with the monkey and then gestured toward the box with the food by jerking his head toward that box. This process was repeated for a total of 40 rhesus monkeys. It turned out that 25 of the 40 monkeys correctly went to one of the two boxes the researchers pointed towards. a) State the appropriate null and alternative hypotheses in the context of this study, first in words and then in symbols. (2 pts) b) Find the p-value using a theory-based test (one-proportion z-test; normal approximation). Show the commands and/or calculations you used to justify your numeric p-value. Be sure to record the information & your p-value below. (6 pts) Probability of success (p): Sample size (n): p-value = c) Make your decision and summarize your conclusion from your p-value. (Assume an "Alpha = 0.05" for your decision) (4 pts) d) What is the z-statistic for the test? What does this number represent in the context of this study? Be sure to show your calculations. (3 pts)