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). Th en 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 oft en than what would be done by random chance.
a. Describe the parameter of interest in the context of this study and assign a symbol to denote it.
b. What is the observed value of the statistic in this case?
c. Write out the null and alternative hypotheses for this first in words and then in symbols.
d. We conducted a test of significance using the One Proportion applet and got the following null distribution for the €œnumber 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?

e. 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.
f. 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 €¦
g. What does a single dot in the null distribution represent in terms of Sarah and the photos?

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0.5 Probability of heads: Number of tosses: Number of repetitions: [100 [ Animate Toss Coins Total = 100 40 30 10 3 4 5 6 7 8 Number of heads