Question Two [6 marks] The Human Resources department at the hospital where the Emergency care unit is located has a formula that it has used to allocate staff to the Emergency care unit. This formula is based on both the "day of the week" and the "time of the year". We call the number of staff that are allocated on each of the 100 days in our sample the Y variable. Julia would like to know what if any relationship there is between the X variable i.e. the number of patients who attend the Emergency care unit and the Y variable i.e. the number of staff that Human Resources have allocated to the Emergency care unit that day. If there is evidence that there is no relationship or a very weak relationship then Julia will argue that the rule used by Human Resources to determine staff levels needs to be changed. For our sample of 100 days for the X variable we saw in Question 1 that Ex, = 4037 and Ex, =172403 For the Y variable in this question 100 Ly. = 1102 and Ev, = 13172 and Sy=3.2223 The sum of the cross products for the two variables is Ex.y, = 47004 7-1 (a) Find the unbiased sample estimate of the covariance and state what this value is telling us about the relationship between these two variables. [2 marks] (b) Find the correlation coefficient and briefly discuss what this value is telling you about the relationship between these two variables. Does this result indicate that the rule used by Human Resources to allocate staff does not help the hospital to allocate the appropriate number of staff to the Emergency care unit on different days. [3 marks] (c) What diagram should be used here to show whether these two variables are related and how strongly they are related. From the answer to part (b) what would you expect this graph to look like. [1 mark] Question 2 Total marks : 6 = 2+3+1