1. The most common therapy for ngernail warts is cryotherapy, in which liquid nitrogen is applied to the area of the wart every few weeks, freezing it for a few seconds until the wart falls off. An alternative therapy is to put duct tape on the wart and leave it there for a week at a time until the wart goes away. In a randomized trial, 51 patients with ngernail warts were randomly assigned to a cryotherapy treatment or a duct-tape treatment. Of 26 patients treated with duct tap e, 22 had their warts completely cured. With the liquid nitrogen treatment, 15 of 25 patients were cured of their warts. a. [5 points) Conduct a hypothesis test to see if there is a difference in efcacy between cryotherapy and duct tap e, in treating ngernail warts. Write the hypotheses, calculate the test statistic, show the rejection region, and make a decision. Also calculate and report the P-value for your test. Write a conclusion. Observed Cured Not Cured Total Duct tape 22 4 26 Nitrogen 15 10 25 Total 37 14 51 b. [1 point) How much more likely is a patient to be cured using duct tape compared to cryotherapy? c. [0.5 pt) Calculate the odds of being cured using duct tape. d. [0.5 pt) Calculate the odds of being cured using cryotherapy. e. [1 pt] Calculate and interpret the odds ratio for being cured, comparing duct tape to cryotherapy. 2. In a test of Murphy's Law, pieces of toast were buttered on one side and then dropped. Murphy's Law predicts that they will land butter-side down. Out of 982 total slices of toast, 610 landed butter-side down. Does this nding provide evidence in favor of Murphy's Law? [You can set this up as a two-sided alternate hypothesis) a. [1.5 pt) State your hypotheses and dene your parameters of interest. b. [2.5 pt) Calculate the test statistic, rejection region, and make a decision using the rejection region. c. [1 pt] Find the P-value and state your decision using the P-value. d. [0.5 pt] Write your conclusion