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 pointed and looked toward the box that contained the food. Th is process was repeated for a total of 40 rhesus monkeys. It turned out that 31 of the monkeys approached the box that the human had gestured toward, and 9 approached the other box. Th e purpose is to investigate whether rhesus monkeys can interpret human gestures better than random chance.
a. Identify the observational units and variable in this study. Also classify the variable as categorical or quantitative.
b. Describe in words the parameter of interest for this study and assign a symbol to it.
c. Determine the sample proportion of monkeys who picked the box towards which the human had gestured. Is this value a parameter or a statistic? What is the symbol you should use to denote this proportion?
d. State the appropriate null and alternative hypotheses in the context of this study, first in words and then in symbols.
e. Describe how you could use a coin to conduct a simulation analysis of this study and its result. Give sufficient detail that someone else could implement this simulation analysis based on your description. Be sure to indicate how you would decide whether the observed data provide convincing evidence that rhesus monkeys can interpret human gestures better than random chance.
f. Use an applet to conduct a simulation analysis with at least 1,000 repetitions. Based on the null distribution produced by the applet, explain how you are deciding whether the observed data provide convincing evidence that rhesus monkeys can read human gestures better than random chance. Summarize the conclusion that you would draw about the research question of whether rhesus monkeys have some ability to understand gestures made by humans.