Using R Studio:

In an experiment to test an animals sense of smell, animals had the choice of turning to the left or to the right at the end of a passage. There was food hidden either to the right or to the left. Of the 12 animals tested, 9 turned toward the food. We wish to test whether the animals were choosing a direction at random, or whether they were able to smell the presence of the food.

a. What is the null hypothesis?

b. Use the binomial functions in R to calculate the probability of exactly 9 out of 12 animals turning toward the food given the null hypothesis is true.

c. Make a barplot of the null distribution of the number of animals turning toward the food, with appropriate x and y axis labels.

d. What is the exact p-value according to the 2-sided binomial test? Which probabilities from the plot are included in the P value?

e. What is your conclusion from this test?

f. What is the 95% confidence interval of the proportion turning toward the food, according to the binomial test?

g. What is the agresti-coul confidence interval?