Name: [20 points] Written Quiz F (Sections 6.2-0, 6.2-CI, 8: 6.2-HT} STA 270: Applied Statistics 1. In a random sample of 50 baseball games, the mean length of the games is 179.83 minutes with a standard deviation of 26.52 minutes. You will do both a hypothesis test and a confidence interval for this scenario, to practice both skills. Part 1 - Does this sample provide evidence that g, the mean length of time for all baseball gamesI is more than 170 minutes? Use a standardized test statistic and the normal distribution. Show all details of the test. a. [2 pts] Set up the null and alternative hypothesis. You do not have to define the parameter. b. [3 pts] Compute the t test statistic using the formula shown in section 6.2-HT. Show all work. c. [3 pts] What is the p-value of the test? You can use the theoretical distribution in Statkey, or the t-distribution table, as explained from sections 5.1/5.2 d. [3 pts] Give the conclusion of this hypothesis test In context at the alpha = 0.10 level. Part 2 Construct a 90% confidence interval for g = the true average length of all baseball games. a. [1 pt] What is the degrees of freedom for this scenario? I. [2 pts] What is the t-critical value for this scenario? 3. [3 pts] Construct a 90% Cl using the formula shown in section 6.2-Cl. Do not interpret this interval. Show all work. h. [3 pts] Compare the results of the HT to the Cl. How are the results consistent