Hermit crabs fight for ownership of shells. Fights are initiated when one crab r
ID: 3290774 • Letter: H
Question
Hermit crabs fight for ownership of shells. Fights are initiated when one crab raps on the shell of another with its big claw. An exchange of shells occurs approximately 50% of the time. Investigators wish to see if the rapping force helps decide the issue. They set up an experiment with a rubberized shell, which would dampen the force of the rapping. They reason that the reduced force should result in fewer exchanges of shells. They then observed 59 fights to see how many shell exchanges occurred. a) What null and alternative hypotheses should the investigators use? In a few sentences, justify your choice of the alternative hypothesis b) Describe a Type I and Type II error in this context.
Explanation / Answer
a) H0: p>=0.5 (proportion of shell exchange in the fight is greater than or equal to standard 50%; this is just opposite of null hypothesis)
Ha: p<0.5 (proportion of shell exchange in the fight is less than the standard 50% )
The alternate hypothesis is so designed that it should describe the question in hand. The claim is that the shell exchange will reduce in proportion (from 50%) which will be Ha; opposite of which will be H0 saying that there is no significant reduction in shell exchange.
b) Type-I error: when we reject the H0 given it's actually true. In this case if actually there is no significant reduction in shell exchange but we conclude that there is significant reduction, we commit type-I error.
Type-II error: when we don't reject the H0 given it's actually false. In this case if actually there is significant reduction in shell exchange but we conclude that there is no significant reduction, we commit type-II error.