l. (4 points) Suppose that a researcher has collected some data and calculated a sample mean of l7 = 32.8 and a sample standard deviation of s = 24.1 om a set of 49 observations. a. (1 point) From previous work, it was determined that the population mean ,u is less than or equal to 33. Conduct a hypotheses test to determine if these data provide enough evidence to conclude that the population mean is actually greater than 33. Show all seven steps of the hypothesis tes; and conduct the test at a = 0.05 . I b. (1 point) Within the context of this test, explain what a Type I error is. Given the test statistic value calculated in a.), please state how likely you think it is that a Type I error occurred. c. (2 points) Calculate the probability of a Type H error if the actual mean of the population, 1.1\" , is 36. As part of this draw the density function for the distribution under the null hypothesis and then also draw the density function assuming pa is 36. On these density functions show the rejection region and shade in the area that corresponds to the probability of a Type 11 error