this additional research? 2. Consider the following scenarios where you have collected a sample of some quantity of interest and you are interested in performing a hypothesis test to verify a claim about this quantity of interest. In each of the scenarios below, write down: I Whether the claim pertains to a true mean ,u or a true proportion 33; a What the null and the alternate hypothesis are-T In What connnands} in R you use to run the hypothesis test; a What the p-value is, a Whether you reject or fail to reject the null hypothesis; and I What you conclude about the original question. In each problem, you may assume a signicance level of or = 0.05. (a) At a manufacturing plant, a manager suspects that the defect rate for a part is too high. The plant's target is to have a defect rate of 3% or lower. He tests a sample of 4000 parts, and finds 345 parts out of 4000 are defective. Based on this sample information, is the defect rate higher than the target of 8%? {b} A mayoral candidate needs more than 50% of the city's voters to vote for her in order to be elected. Her campaign team polls a random sample of SDI) voters, and nds that 460 voters plan to vote for her. Based on this sample, will the candidate win the election? {c} A fast food restaurant is concerned that too much food is being wasted, due to improper handling, refrigeration and preparation. For a period of 50 days, it measures the pounds of food wasted each day. This data is provided in the le fastfood.csv, mider the column dailymaste. The restaurant's target is to waste, on average, no more than ll pounds per day. Based on this sample, is the fast food restaurant wasting more food than its desired target? {d} An online retailer is considering implementing a new markdown pricing algorithm. To test it, it runs a eld experiment with the new algorithm for 3|] of its product categories over a one month period. For each product category, it measures the percentage change in revenue relative to a benchmark monthly revenue for that product category based on the incumbent markdown pricing approach. The data is provided in the le markdownpricing. csv, under the column percentage . change. Based on this sample, should the retailer adopt the new markdown pricing algorithm