8. (a) A random sample of 1,793 students from various areas is taken to compare the performance of students in Statistics, based on the final examination mark (low:below 40%, medium:

between 40% and 60%, high: above 60%), in relation to the amount of revision they undertook. The results are summarised in the table below. Calculate the x² statistic and use it to test for a relationship between performance in Statistics and amount of revision. Testing at the 1% significance level only, would you conclude that revision improves the performance in Statistics? Justify your answer. (b) A manager is considering how useful an ability test in sales is on newly hired employees in the company. For this reason 10 randomly chosen employees took the test before they started working in the company. Summary statistics for the test scores (x values) and the values of the sales for these employees during the first month of working at the company (y values, in hundreds of dollars) are: i. Calculate the least squares line of y on x. ii. Based on the regression equation in i., what level of sales would you predict from an employee who scored 4.0 on the ability test? marks)iii. What additional information would you need to decide whether your prediction in ii. is reliable? Explain your answer. iv. Using a 1% significance level, test whether test scores, æ, affect the value of sales,y.