Question 1: A new filtering device is installed in a chemical unit. Before its installation, a random sample is taken and yielded the following information about the percentage of impurity: y1. = 12.5, s; = 101.17, and n, = 10. Then after installation, a random sample is taken and yielded y2. = 10.2, s; = 94.73, and n2 = 10. a. (1 pt.) In this experiment, the two samples are independent or dependent? b. (2 pts) The two variances should be assumed equal or not (of = oz or of # o? ) and why? c. (3 pts) Test that the filtering device reduced the percentage of impurity significantly at significance level 5% (a = 0.05). You can answer this question by using the confidence interval of the difference between the two population means or using the test of hypothesis approach. Also keep in your mind that your assumption in (b) affects your answer for (c)