Question 1: [40 Marks] I. Consider diamonds dataset, which can be found in the working dataset on the Moodle page or https://github.com/shazizisazi/Datasets. Using an appropriate hypotheses testing check whether two attributes 'color' and 'cut' are independent at the significant level 0.01? To do so, (20) a) State the null and alternative hypotheses. b) Compute the test statistic-value. c) Find the critical-value. d) Identify the decision rule and express your decision. II. Find 95% confindence interval for the varible 'price' and interpert that from a business prespective. (10) III. Can we conclude that different categories of 'cut' has the same probability to be observed at the confindence level 0.95.? Demonstrate your answer with an appropriate hypotheses testing