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 3 Date 1/25 3/19 5/30 7/3 9/13 11/7 Initial Depth, X 63.3 40.2 49.4 45.1 46.4 68.2 Depth Five Years Later, Y 62.2 40.0 45.6 46.0 40.5 70.8 a) Why is it important to take the measurements on the same date? ow A. Using the same dates makes the second sample dependent on the first and reduces variability in water clarity attributable to date. B. Using the same dates maximizes the difference in water clarity. C. Using the same dates makes it easier to remember to take samples. D. Those are the same dates that all biologists use to take water clarity samples. b) Does the evidence suggest that the clarity of the lake is improving at the a = 0.05 level of significance? Note that the normal probability plot and boxplot of the data indicate that the differences are approximately normally distributed with no outliers. Let d = X,- Yj. Identify the null and alternative hypotheses. Но: Hy: ITune integers or decimals Do not round Click to select your answer(s). back 8. 5162 S55-7361 EG4S Low P. Mut arch or type URL +) & ( ) 8 delete { } | [ ] н K return ? 2. * 00 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 2 4 6. Date 1/25 3/19 5/30 7/3 9/13 11/7 Initial Depth, X 63.3 40.2 49.4 45.1 46.4 68.2 Depth Five Years Later, Y 62.2 40.0 45.6 46.0 40.5 70.8 Determine the test statistic for this hypothesis test. op Now (Round to two decimal places as needed.) Find the P-value for this hypothesis test. P-value = |(Round to three decimal places as needed.) What is your conclusion regarding Ho? I O A. Do not reject Ho. There is sufficient evidence at the a = 0.05 level of significance to conclude that the clarity of the lake is improving. B. Do not reject Ho. There is not sufficient evidence at the a = 0.05 level of significance to conclude that the clarity of the lake is improving. C. Reject Ho: There is sufficient evidence at the a = 0.05 level of significance to conclude that the clarity of the lake is improving. Click to select your answer(s). Feedback 5162 8. 355-7561 EG4S +, Q Search or type URL & ( ) 8 delete { } | Y [ ] н J K return く ? | shift P. 2. ト