Question

3. A new purification unit is installed in a chemical process. Before its installation, a random sample was gathered from the purification unit and yielded the following data about the measure of impurity: x = 25.61 .si = 5.39 . n = 14 After installation, a random sample resulted in: .X2 = 23.02 . sz = 4.35 • n2 = 16 Can you conclude that the new purification device has reduced the mean measure of impurity? (20 pts) a. Report your null and alternative hypothesis. b. State the results (including: p-value, calculated test statistic, and confidence interval) c. State the rejection decision d. State reasoning for decision e. What does the decision in mean with regards to situation (i.e. Can you conclude that the new purification device has reduced the mean level of impurity?)

Answer 1

solution a Here let Sample 1 is before installation I let Sample 2 is after installation Hol, = 42 S Hi M, alla b) Given ni= 14, 2x1 = 25.61, 87 = 5.39 mg = 16, ły = 23.02, 8z = 4:35 80= MD st (2) 5 13(5.39)+15 (4:35) = 4.833 nitra 2 - 14+16-2 S.E 55 ( 1 ) = Ju.833 (tutte) = 0.8045 Test statistic t = x1-42 = 25.61-2302 _ 3:22 d-f=nt nitna -2=14+16-2=28, Rita P-value=0.0016 25.61- 23.02 3.22

At 95% confidence toje 2.008 The 95% C I for difference es (01-12 + tobe SE = (25-61 – 23.02) + 2018 (0.8045) = 2.59 +1.648=(0.942, u-238) o here P-vodue groot6 2005, so reject to c here the rejection region is het > 1.7011 d) here colt=3.22 >17011, so reject Ho. 2 so we can conclude that the new purification device has reduced the mean measure of empurify.