1. The Nassau Bahamas Community College claims that students who take statistics spend on average 19 hours a week working. The population standard deviation is not known. Statistics students in MAT 102 believe students work more than 19 hours because they want to make more money. A sample of 25 statistics students indicates that they work a sample mean average time of 24.20 hours per week, with a sample standard deviation of 12.59 hours. Using a significance level of 5%, construct a Hypothesis test to determine if the students claim is correct. a. Write the null and alternative hypothesis. You should provide the hypothesis in both full sentence form as well as symbolically. b. Determine the type of distribution you would use for this hypothesis test and why you chose it. c. State whether to reject or fail to reject the null hypothesis and give your reason. Students can use either answer d. Draw a diagram that illustrates the key elements of the hypothesis test and decision rule e. Are the students correct and why