Homework: Ch 11 HW: Two Sample Procedure Question 6, 11.2.10 Part 40f7 HW Score: 56.7%, 9.64 of 17 points O Points: 0.55 of 1 Save A researcher studies water clarity at the same location in a lake on the same dates during the course of a year and repeats the measurements on the same dates 5 years later. The researcher immerses a weighted disk painted black and white and measures the depth (in inches) at which it is no longer visible. The collected data is given in the table below. Complete parts (a) through (c) below. Observation Date Initial Depth, Xi Depth Five Years Later, Yi 1/25 55.1 60.5 2 3/19 61.8 59.3 3 5/30 45.3 45.7 4 713 59.5 56.8 5 9/13 44.6 46.9 6 11/7 49.2 48.1 Click the icon to view the table ot critical t-values. a) Why it important to take the measurements on the same date? using the same dates makes it easier to remember to take samples. Those are the same dates that all biologists use to take water clarity samples. using the same dates maximizes the difference in water clarity. using the same dates makes the second sample dependent on the first and reduces variability in water clarity attributable to date. b) Does the evidence suggest that the clarity of the lake is improving at the 0.05 level ot significance? Note that the normal probability plot and boxplot of the data indicate that the ditterences are approximately normally distributed witn no outliers. Let di = Xi - Yi_ Identity the null and alternative hypotheses. Determine the test statistic tor this hypothesis test 0.24 (Round to two decimal places as needed.) Find the critical value(s) for this hypothesis test (use a comma to separate answers as needed. Round to two decimal places as needed.)