Question

1.3.16 Rhesus monkeys 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 30 of the monkeys approached the box that the human had gestured toward, and 10 approached the other box. The purpose is to investigate whether rhesus monkeys can interpret the head jerk better than random chance.

Which of the following null hypothesis and alternative hypothesis are appropriate in the context of the study?

a. Null: The long-run proportion of times that rhesus monkeys choose the correct box is 50%. ​Alt. The long-run proportion of times that rhesus monkeys choose the correct box is 50%.

b. Null: The long-run proportion of times that rhesus monkeys choose the correct box is 50%. ​Alt. The long-run proportion of times that rhesus monkeys choose the correct box is less than 50%.

c. Null: The long-run proportion of times that rhesus monkeys choose the correct box is 50%. ​Alt. The long-run proportion of times that rhesus monkeys choose the correct box is greater than 50%.

d. Null: The long-run proportion of times that rhesus monkeys choose the incorrect box is 50%. ​Alt. The long-run proportion of times that rhesus monkeys choose the incorrect box is greater than 50%.

Determine the standardized statistic from the data. (Hint: You will need to get the standard deviation of the simulated statistics from the null distribution in an applet.) (Round answer to 2 decimal places, e.g. 52.75)

Which of the following is the best interpretation of the standardized statistic in the context of this study?

a. The number of standard deviations the observed proportion is below 0.50 in the null distribution.

b. The number of standard deviations the observed proportion is above 0.75 in the null distribution.

c. The number of standard deviations the observed proportion is above 0.50 in the null distribution.

d. The number of standard deviations the observed proportion is below 0.75 in the null distribution.

Select the best conclusion that you would draw about the research question of whether rhesus monkeys have some ability to understand gestures made by humans.

a. We have no evidence that the long-run proportion of times that rhesus monkeys choose the correct box is greater than 50%.

b. We have strong evidence that the long-run proportion of times that rhesus monkeys choose the incorrect box is greater than 50%.

c. We have weak evidence that the long-run proportion of times that rhesus monkeys choose the correct box is greater than 50%.

d. We have strong evidence that the long-run proportion of times that rhesus monkeys choose the correct box is greater than 50%.

Answer 1

Which of the following null hypothesis and alternative hypothesis are appropriate in the context of the study?
c. Null: The long-run proportion of times that rhesus monkeys choose the correct box is 50%. ​Alt. The long-run proportion of times that rhesus monkeys choose the correct box is greater than 50%.

We need to test if the proportion of the rhesus monkeys chooses the correct box between than random chance.

In this case, the monkey has two options, to choose the correct box or to choose the wrong box. Hence probability for either of the choice is 50%. Hence random chance here is 50%.
Hence the alternative hypothesis is whether the proportion is greater than 50%

Determine the standardized statistic from the data. (Hint: You will need to get the standard deviation of the simulated statistics from the null distribution in an applet.) (Round answer to 2 decimal places, e.g. 52.75)

Which of the following is the best interpretation of the standardized statistic in the context of this study?(note this is an approximate answer, you need to simulate in the applet. Since details of the applet is not given cannot really work it out)
b. The number of standard deviations the observed proportion is above 0.75 in the null distribution.

Select the best conclusion that you would draw about the research question of whether rhesus monkeys have some ability to understand gestures made by humans.

d. We have strong evidence that the long-run proportion of times that rhesus monkeys choose the correct box is greater than 50%.

The detailed solution is given below.