Calculation practice: Binomial test. Do people typically use a particular ear preferentially when listening to strangers? Marzoli and Tomassi (2009) had a researcher approach and speak to strangers in a noisy nightclub. An observer scored whether the person approached turned either the left or right ear toward the questioner. Of 25 participants, 19 turned the right ear toward the questioner and 6 offered the left ear. Is this evidence of population difference from 50% for each ear? Use the following steps to help answer this question with a binomial test. Assume that the assumptions of the binomial test are met in this study.

a. State the null and alternative hypotheses for the binomial test.

b. What is the observed value of the test statistic?

c. Under the null hypothesis, calculate the probability of getting exactly 19 right ears and 6 left ears.

d. List all possible outcomes in which the number of right ears is greater than the 19 observed.

e. Calculate the probability under the null hypothesis of each of the extreme outcomes listed in (d).

f. Use the addition rule to calculate the probability of 19 or more right eared turns under the null hypothesis.

g. Give the two-tailed P-value based on your answer to (f).

h. Interpret this P-value What does it indicate?

i. State the conclusion from your test.