A nutritionist wants to investigate if a new diet leads to improved weight loss in a 6 month period. Previous studies have shown that people can lose an average of about 20 pounds in 6 months. Researchers recruit 50 randomly selected people who struggle to lose weight participate in a study where they record their starting weight prior to using the diet and then their weight in 6 months after using the new diet plan. Among the 50 people, the average amount of weight lost was 35 pounds with a sample standard deviation of 5 pounds. Conduct a test at the = 0.05 level to assess the effectiveness of the new diet. (a) Set up the null and alternative hypothesis (using mathematical notation/numbers AND interpret them in context of the problem). (b) Calculate the test statistic. (c) Calculate the critical value. (d) Draw a picture of the distribution of the test statistic under H0. Label and provide values for the critical value and the test statistic, and shade the critical region. (e) Make and justify a statistical decision at the = 0.05 level and state your conclusions in context of the