Recall Exercise 1.2.30 about chimpanzees having a sense of number. Besides testing Mercury, the researchers also tested three other chimpanzees. One, named Lana, picked the container that held 4 bananas (rather than the one with 3 bananas) 14 times out of 20. Do these data provide evidence that Lana is more likely than not to pick the container with more bananas in it in the long run? 

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

b. Use the One Proportion applet to find a p-value for this test. 

c. Would you say that we have strong evidence that Lana tends to pick the container with more bananas? How are you determining this?

Data from Exercises 1.2.30

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 shown.

 

Transcribed Image Text:

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