Introduction- Introduce the business problems. (10 marks) What are your reasons for the variables you choose for the analysis What are your reasons for using analytical methods that you will employ Binomial distribution (10 marks) Calculate Binomial probabilities where number of trials n=10, probability of success p=0.5, x=1,2,...,10. Z scores calculation (10 marks) Calculate z scores for age and annual income and interpret the results by identifying outliers. (outside of -3 to +3) A test of chi-square for independence (20 marks) Are two categorical variables of type of use and loyalty independent? Formulate the statistical hypothesis to test this Run a statistical test of the hypothesis Interpret your test result Using below table show your calculation of expected value of i (ei) for each cell and show chi-square of a with the degree of freedom. For this exercise a=0.05 Type of use/loyalty 1 2 3 4 Total 1 Qi= 10 15 11 16 2 15 22 10 16 3 13 18 19 17 Total Relationship between multiple numerical variables (20 marks) Correlation: Create a scatter plot of opening gross sales and revenue and interpret it We would like to find out whether annual income of employees depends on the revenue of the business. Calculate the correlation coefficient between annual income and revenue Interpret the calculated correlation coefficient Regression: Run a regression analysis of annual income and revenue Interpret the regression output Discussion of the results and recommendations (10 marks) This includes discussion of the findings and conclusion.Marital status Gender Promotion Type of use Region Payment Source Product Loyalty Married=1 Male=1 Supervisor=1 Light user=1 East=1 Paypal=1 Web=1 DVD=1 not loyal Single=2 Female=2 Manager=2 medium userl=2 West=2 Credit=2 Email=2 CD=2 somewhat loyal Divorced=3 Department mar Heavy user=3 North=3 cash=3 Shop=3 Novel=3 nutral Widow=4 South=4 Classical=4 somewhat disloyal Politics=5 very loyal Best seller=6