Recall Exercise 1.5.34 that introduced the binomial distribution as an exact theory-based distribution to model the types of situations you have seen in Chapter 1. Two of the other dogs in the research project were Tug and Auggie. When the researcher bowed toward the cup, Tug went to the correct cup 7 out of 10 times and Auggie went to the correct cup 6 out of 10 times. 

a. Find simulation-based, normal approximation, and exact binomial p-values based on Tug’s statistic. How do they compare? 

b. Find simulation-based, normal approximation, and exact binomial p-values based on Auggie’s statistic. How do they compare?

Data from Exercises 1.5.34

In Exploration 1.1 you looked at data involving the dog Harley picking one of two cups that the experimenter bowed toward. Another dog in that study named Jango, a male black lab, went to the cup that the experimenter bowed toward 8 out of 10 times. Does Jango understand bowing? Let π represent Jango’s probability of going to the correct cup. We will test the hypotheses H₀: π = 0.50 and H_a: π > 0.50.