A 2009 study (Marzoli and Tommasi, 2009) investigated whether people are more likely to agree to a request from a stranger if it is spoken into their right ear rather than their left ear. The researchers proposed that the asymmetry of the human brain makes one of our ears more agreeable than the other. How did they do this? They hired students to approach strangers in Italian discos and ask them for a cigarette.

Of course, the unwitting experimental subject could only comply if they were a smoker.

In the study, 88 requests were spoken into right ears, and 88 into left ears. The results were that 34 of the right-ear requests and 17 of the left-ear requests were successful.

At first sight, this study doesn’t seem to fit with our usual binomial testing framework, because there are two sets of results:

one for left ears and one for right ears. Indeed, there are better ways of approaching this analysis. However, with a little ingenuity we can still use a binomial test.

a. Suppose you restrict your analysis to the successful requests only. How many successful trials were there?

b. How many of the successful trials were spoken into right ears, and how many into left ears?

c. If there is no systematic bias in the chance of success for the two different ears, what proportion of the successful trials would you expect to arise from each ear?

d. Set up suitable hypotheses and carry out a hypothesis test for evidence of systematic bias between requests spoken into left and right ears. Interpret your findings.