You have been volunteering at the animal shelter of San Diego. You are curious to know if the length of the shifts volunteers work at the shelter is on average 2 hours. You record the lengths of 30 random shifts worked by volunteers. The shifts have a mean of 1.85 hours and a standard deviation of 0.483 hours. a) [2 points] Define the parameter of interest and the appropriate null and alternative hy- potheses. b) [2 points] Define the appropriate test statistic and calculate its value. You don't need to check assumptions. c) [3 points] Calculate the p-value. (Indicate the correct degrees of freedom. You can indicate an approximate p-value or a range if needed, e.g. 0.2 < p-value < 0.3.). d) [2 points] Write a conclusion. Use significance level 0.05. e) [2 points] What is the type I error in this contest? f) [2 points] What is the type II error in this contest? g) [2 points] What is the probability of type I error of this test? h) [2 points] If you were to construct a 95% CI for the average length of the shifts worked by volunteers, would the CI contain 2? Answer this question without actually constructing the CI but basing your answer solely on the HT conducted. Briefly explain.