2. The data were taken on 20 incoming shipments of chemicals in drums arriving at a warehouse. The data contains the number of drums in shipment (X1), total weight of shipment (X2, in hundred pounds), and number of minutes required to handle shipment (Y). The data was fitted to the following regression model: Y=Bo+BX + B2X12+, i = 1,..., 20. The Fitted results are given below: Estimate Std. Error t value Pr(>|t) (Intercept) 3.3243 3.1108 1.069 0.3 x1 3.7681 0.6142 6.135 1.10e-05 5.0796 0.6655 7.632 6.89e-07 x2 (i) [12 marks] Without looking at the data, what would you suspect on the relationship between the time required to handle shipment, Y, and the total weight of shipment, X2? In other words, do they have a positive or an negative relationship? Formulate an appropriate hypothesis testing to test the relationship: (a) state your null and alternative hypotheses, (b) give the value of the test statistic, (c) obtain the critical value at level a = 0.05, (d) obtain the p-value of the test without using R, and (e) draw your conclusion. (ii) [12 marks] The shipment company wanted to find out that, given the total weight of the shipment, the time needed for handling an additional drum should be less than 5 minutes. Formulate the hypotheses properly to test whether this can be confirmed at level a = 0.05. Provide your null and alternative hypotheses, the formula and value of the test statistic, the p-value of the test. Draw your conclusion based on the p-value.