This assignment is intended to test your knowledge of how to appropriately compare two means. The data file (attached file: data_file.xlsx) has 50 randomly selected student debt amounts from 2018and 50 randomly selected student debt amounts from 2013.The data fields included are as follows:Debt in 2018 (dollars)Debt in 2013 (dollars)A university representative wants to know whether the sample data provide enough evidence to believe there is a difference between the debt amounts in the two years. The null and alternative hypotheses are shown below.Null Hypothesis: Mean Student Debt in 2018 is equal to Mean Student Debt in 2013Alternative Hypothesis: Mean Student Debt in 2018 is not equal to Mean Student Debt in 2013Complete the following tasks:1.Run an F-test for two sample variances using an alpha level of 0.05 and answer the following questions:Which of the two years has the higher mean? What are the values?Which of the two years has the higher variance? What are the values?Based on the statistical output, would you conclude that variances are equal or not equal? Provide an appropriate/authoritative explanation leveraging the statistical output.2.Run an appropriate t-test (assuming either equal or unequal variances based on your conclusion in 1c above) using an alpha level of 0.05and answer the following questions:Is this a one-tailed or two-tailed test? Provide an appropriate/authoritative explanation that fully explains the choice.Based on the statistical output, would you conclude that means are equal or not equal? Provide an appropriate/authoritative explanation leveraging the statistical output.Using everyday language that could be understood by parents and students, what does the analysis say about student debt in 2018versus 2013? Provide an appropriate/authoritative explanation leveraging the statistical output (e.g., use confidence level, rationale, etc.)Make sure that you run all the required analyses using the Data Analysis Toolpak in Excel and SUBMIT the Data Analysis Output along with the Data file in a Single Excel workbook that shows all your output. You should also submit a separate Word document that fully, and professionally, responds to each question.Run all required analyses and submit them along with the data file in a single Excel workbook that shows all your output and provide responses to all of the questions in a Word document.Resourceshttps://www.youtube.com/watch?v=qI_RmXU1tOYhttps://www.youtube.com/watch?v=OHHhzLHakKAhttps://www.youtube.com/watch?v=L-jfenou5hI

Question 1 - Basic Probability (10 marks)According to a recent study, 9 out of 10 parents have helped their adult children with some financial assistance. The following table shows the number of times parents have given their adult children financial assistance to buy a car and to pay the rent.Pay the rentYes NoBuy a car Yes 90 50No 10 150a. Develop a joint probability table. (2 marks)b. Using the marginal probabilities for ‘buy a car’ and ‘pay the rent’, are parents more likely to assist their adult children with buying a car or paying the rent? What is your interpretation of the marginal probabilities? (2 marks)c. If parents provided financial assistance to buy a car, what is the probability that the parents assisted with paying rent? (2 marks)d. If parents did not provide financial assistance to buy a car, what is the probability that the parents assisted with paying rent? (2 marks)e. What is the probability that parents provided financial assistance for their adult children by either helping to buy a car or pay rent? (2 marks)Question 2 – Normal Distribution (10 marks)The time needed to complete a final examination in a particular college course is normally distributed with a mean of 160 minutes and a standard deviation of 20 minutes. Answer the following questions:a. What is the probability of completing the exam in 120 minutes or less? (2 marks)b. What is the probability that a student will complete the exam in more than 120 minutes but less than 150 minutes? (2 marks)c. What is the probability that a student will complete the exam in more than 100 minutes but less than 170 minutes? (2 marks)d. Assume that the class has 120 students and that the examination period is 180 minutes in length. How many students do you expect will be unable to complete the examination in the allotted time? (4 marks)Question 3 – Sampling Distribution (10 marks)The Economics Policy Institute periodically issues reports on wages of entry-level workers. The Institute reported that entry-level wages for male college graduates were $43.36 per hour, and for female college graduates were $37.60 per hour. Assume the standard deviation for male graduates is $2.30 and for female graduates is $2.05.a. What is the probability that a sample of 50 male graduates will provide a sample mean within $0.50 of the population mean, $43.36? (3 marks)b. What is the probability that a sample of 50 female graduates will provide a sample mean within $0.50 of the population mean, $37.60? (3 marks)c. In which of the preceding two cases, part (a) or part (b), do we have a higher probability of obtaining a sample estimate within $0.50 of the population mean? Why? (2 marks)d. What is the probability that a sample of 120 female graduates will provide a sample mean more than $0.30 bel