Your organization has recently introduced a training program, through which employees are trained on using a new program to fix bugs in software. To investigate whether the training has increased or decreased average performance, data have been gathered for a matched sample of 50 employees on their performance before and after training. The relevant task of the employees is measured in terms of the number of software bugs they fix per day. Before the introduction of the training, performance has an average of 36.2 fixes per day, while after the plan's introduction, performance has an average of 39.6 fixes per day. The standard deviation of the performance difference is 7.37. a. Formulate the null and alternative hypotheses to test whether performance has improved due to the introduction of the training program. (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 training program increase employee performance? Use the critical value approach. (5 marks)