Your organization has recently introduced an incentive plan, through which the pay of employees is coupled to their performance. To investigate whether the introduction of the incentive plan has increased or decreased average performance, data have been gathered for a matched sample of 60 employees on their performance before and after the introduction of the incentive plan. The relevant task of the employees is measured in terms of the number of customers they serve per day. Before the introduction of the incentive plan, performance has an average of 43 customers per day, while after the plan's introduction, performance has an average of 46 customers per day. The standard deviation of the performance difference is 8.67. a. Formulate the null and alternative hypotheses to test whether performance has changed due to the introduction of the incentive plan. (5 marks) b. Calculate the test statistic. What is the number of degrees of freedom for the relevant sampling distribution? (5 marks) c. At 95% confidence, did the introduction of the incentive plan change employee performance? If so, did performance increase or decrease? Use the critical value approach. (5 marks) d. Calculate the 99% confidence interval for the mean difference. Does the confidence interval suggest that the null hypothesis should be rejected