A sample of dogs were trained using a ?Do as I do? method, in which the dog observes the trainer performing a simple task (such as climbing onto a chair or touching a chair) and is expected to perform the same task on the command ?Do it!? In a separate training session, the same dogs were trained to lie down regardless of the trainer?s actions.

Later, the trainer demonstrated a new simple action and said ?Do it!? The dog then either repeated the new action, or repeated a previous trained action (such as lying down). The dogs were retested on the new simple action after one minute had passed, and after one hour had passed. A ?success? was recorded if a dog performed the new simple action on the command ?Do it!? before performing a previously trained action.

The article ?Your Dog Remembers More Than You Think? (Science, November 23, 2016, sciencemag.org/news/2016/11/your-dog-remembers-more-you -think, retrieved May 6, 2017) reports that dogs trained using this method recalled the correct new action in 33 out of 35 trials. Suppose the data from this study will be used to determine if more than half of all dogs trained using this method would recall the correct new action.

a. Explain why the data in this example should not be analyzed using a large-sample hypothesis test for one population proportion.

b. Perform an exact binomial test for the null hypothesis that the proportion of all dogs trained using this method who would perform the correct new action is 0.5, versus the alternative hypothesis that the proportion is greater than 0.5.

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Binomial Distribution 0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.01 20 40 60 80 Successes 100 120 140 160 Null Hypothesis Observed Sample Proportion P-Value 0 200 0.093 0.000 Probability