Underwater sound-locating ability of alligators. Alligators have shown the ability to determine the direction of an airborne sound. But can they locate underwater sounds? This was the subject of research published in the Journal of Herpetology (Dec. 2014). Alligators inhabiting the flood control canals in the Florida Everglades were monitored for movement toward a sound produced from a submerged diving bell. Movements within a 180° arc of the direction toward the sound were scored as movements toward the sound; all movements in other directions were scored as movements away from the sound. Consequently, the researchers assumed that the proportion of movements toward the sound expected by chance is 180°>360° = .5. In a sample of n = 50 alligators, 42 moved toward the underwater sound.

a. Give the null and alternative hypotheses for testing whether the true proportion of alligators that move toward the underwater sound is higher than expected by chance.

b. In a sample of n = 50 alligators, assume that 42 moved toward the underwater sound. Use this information to compute an estimate of the true proportion of alligators that move toward the underwater sound.

c. Compute the test statistic for this study.

d. Compute the observed significance level (p-value) of the test.

e. Make the appropriate conclusion in the words of the problem.