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ECO 45 - 011 — Statistical Methods Felipe A. Araujo Spring, 2022 Problem set # 9 (due on April 26, 2021 @ 12:10pm) 1. According to the National Beer Wholesalers Association, U.S consumers 21 years and older consumed 26.9 gallons of beer and cider per person in 2017. A distributor in Milwaukee believes that beer and cider consumption are higher in that city. A sample of consumers in Milwaukee will be taken, and the sample mean 2017 consumption of beer and cider used to test the following null and alternative hypotheses: H,: > 26.9 a. Assume the sample data led to the rejection of the null hypothesis. What would your conclusion be about the consumption of beer and cider in Milwaukee? b. What is the Type | error in this situation? Explore the consequences of making a Type | error in this scenario. c. What is the Type Il error in this situation? Explore the consequences of making a Type Il error in this scenario. 2. Suppose a new production method will be implemented if a hypothesis test supports the conclusion that the new method reduces the mean operating cost per hour. a. State the appropriate null and alternative hypothesis if the mean cost of the current production method is $ 220 per hour. b. Whatis the Type | error in this situation? Explore the consequences of making this error in this situation. c. What is the Type Il error in this situation? Explore the consequences of making this error in this situation. 3. Consider the following hypothesis test: HO:# 2 20 Hy:u <20 A sample of 50 observations provided a sample mean of 19.4 The population standard deviation is 2. What is the relevant sampling distribution for the hypothesis test? Compute the value of the test statistic. What is the p-value? Using a significance level of 5%, what is your conclusion about the null hypothesis? oo o w