2. Large sample test about a population proportion, p. 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 that dampens the force of the rapping. They reasoned that the reduced force should result in fewer exchanges of shells. They then observed 73 fights to see how many shell exchanges occurred. From their study, they observed that 42 of the 73 fights resulted in an exchange of shells. a) What is the variable to be studied and what is the scale of measurement for the variable? b) State in words the null and alternative hypotheses that you would use to address the research question. In one sentence, justify your choice for the alternative hypothesis. c) State the Type I & Type II errors specific to this problem and based on these errors, choose a Type I error level to use for a statistical test about the difference in means. What is your rationale for the chosen Type I error level? d) Sketch the null distribution and state what you assume about the distribution. Provide evidence to justify your assumptions. e) Indicate on the sketch the rejection region(s) for the test. f) Provide the critical value(s) for the test and add the value(s) to your sketch. g) Conduct the test and make a decision about the null hypothesis (reject or fail to reject) h) Based on the test results, what conclusion do you draw regarding the true value of the population parameter? 2. Large sample test about a population proportion, p. 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 that dampens the force of the rapping. They reasoned that the reduced force should result in fewer exchanges of shells. They then observed 73 fights to see how many shell exchanges occurred. From their study, they observed that 42 of the 73 fights resulted in an exchange of shells. a) What is the variable to be studied and what is the scale of measurement for the variable? b) State in words the null and alternative hypotheses that you would use to address the research question. In one sentence, justify your choice for the alternative hypothesis. c) State the Type I & Type II errors specific to this problem and based on these errors, choose a Type I error level to use for a statistical test about the difference in means. What is your rationale for the chosen Type I error level? d) Sketch the null distribution and state what you assume about the distribution. Provide evidence to justify your assumptions. e) Indicate on the sketch the rejection region(s) for the test. f) Provide the critical value(s) for the test and add the value(s) to your sketch. g) Conduct the test and make a decision about the null hypothesis (reject or fail to reject) h) Based on the test results, what conclusion do you draw regarding the true value of the population parameter