Recall Exercise 1.2.19, where researchers investigated whether rhesus monkeys have some ability to understand gestures made by humans. In one part of the study, they found that 31 of 40 monkeys correctly went to one of two boxes that researchers pointed towards.
a. State the appropriate null and alternative hypotheses in the context of this study, first in words and then in symbols.
b. Using an appropriate applet, find the p-value using a theory-based test (one-proportion z-test; normal approximation).
c. Summarize your conclusion from your p-value.
d. What is the z-statistic for the test? What does this number represent in the context of this study?
e. Without using an applet, determine the value of the theory-based (normal approximation) p-value if we used a two-sided alternative hypothesis.