Many types of studies have been done to see whether animals have a sense of number. In one study (Beran & Beran, 2004), researchers wanted to see whether chimpanzees could remember how many items were added to a container when they see them added one at a time. To do this they had two containers set up so the chimpanzees could not see inside them. They randomly added bananas to the containers one at a time and then had the chimpanzees choose the container they wanted. In one set of experiments, they added 3 bananas to one container and 4 to the other and had a chimpanzee named Mercury pick which container he wanted. In 20 trials, he picked the container containing 4 bananas 16 times (or 80%). Do these data convince you that Mercury is more likely to pick the container with more bananas in it in the long run? A null distribution, with 100 repetitions, for testing this situation is show

a. Write out the null and alternative hypotheses for this study in words. 

b. Let π be the long-run proportion of times Mercury picks the container with more bananas. Write out the null and alternative hypotheses for this study in symbols. 

c. Based on the null distribution shown (that has 100 repetitions), what is the p-value for your test? 

d. Would you say that we have strong evidence that Mercury is not just randomly picking a container but has a sense of which container contains more bananas? How are you determining this? 

e. Using the null distribution shown, what is the smallest proportion of times that Mercury picks the container containing 4 bananas so you would say there is strong evidence that Mercury is more likely to pick the container with more bananas in it in the long run?  

Transcribed Image Text:

Probability of heads: Number of tosses: Number of repetitions: 100 Animate Draw Samples Total = 100 18 12 6 0.5 20 0 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 Proportion of heads