A chimpanzee named Sarah was the subject in a study of whether chimpanzees can solve problems. Sarah was shown 30-second videos of a human actor struggling with one of several problems (for example, not able to reach bananas hanging from the ceiling). Then Sarah was shown two photographs, one that depicted a solution to the problem (like stepping onto a box) and one that did not match that scenario. Researchers watched Sarah select one of the photos, and they kept track of whether Sarah chose the correct photo depicting a solution to the problem. Sarah chose the correct photo in seven of eight scenarios that she was presented.

We want to run a test of significance to determine whether Sarah understands how to solve problems and will thus pick the photo of the correct solution more often than what would be done by random chance.

We conducted a test of significance using theOne Proportionapplet and got the following null distribution for the "number of heads." (Note:this null distribution uses only 100 simulated samples and not the usual 1,000 or more.) Based on the null distribution, what is the p-value for the test? How did you calculate it?

Probability of heads: 0.5

Number of tosses: 8

Number of repetitions: 100

Total = 100

1. Based on your p-value, do you have strong evidence that Sarah understands how to solve problems similar to those she was presented? How are you deciding? Justify.
2. Complete this sentence describing what the p-value means: If Sarah doesn't understand how to solve problems and is just guessing at which picture to select, the probability she would ...
3. What does a single dot in the null distribution represent in terms of Sarah and the photos?