College of Public Health and Human Sciences H220: Introduction To Health Data Analysis Spring 2016 Instructor: Harold Bae, PhD, MS (Assistant Professor, Biostatistics) TA: Erin Buth Score: ______ / 20 Due Date: May. 19, 2015 Homework 6 1. Among coffee drinkers, men drink a mean of 2.5 cups per day with a standard deviation of 0.5 cups. Assume the number of drinking per day follows a normal distribution. a. What is the probability that a man drinks less than 1.2 cups per day? (2pt) b. What is the probability that a man drinks between 1.2 cups and 3 cups per day? (2pt) c. What is the probability that the mean number of cups in a sample of 20 men is less than 2.3 cups per day? (3pt) d. What is the probability that the mean number of cups in a sample of 50 men is less than 2.3 cups per day? (3pt) 1 College of Public Health and Human Sciences H220: Introduction To Health Data Analysis Spring 2016 Instructor: Harold Bae, PhD, MS (Assistant Professor, Biostatistics) TA: Erin Buth 2. The mean lifetime for cardiac stents is 8.9 years. A medical device company has implemented some improvements in the manufacturing process and hypothesizes that the lifetime is now longer. A study of 40 new devices reveals a mean lifetime of 9.7 years with a standard deviation of 3.4 years. Is there statistical evidence of a prolonged lifetime of the stents? Follow the five steps (below) to run the appropriate test at a 5% level of significance. a) Set up null and research hypotheses. (2pt) b) Select the appropriate test statistic. (2pt) c) Set up the decision rule. (2pt) d) Compute the test statistic. (2pt) e) Draw a conclusion and summarize significance. (2pt) 2