Question

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 1 2 3 5 6 Date 1/25 3/195/30 7/3 9/13 11/7 Initial Depth, X 52.2 66.7 504 705 55.5 49.2 Depth Five Years Later, 58.5 62.9 55.1 68.0 62.7 47.9 Click the icon to view the table of critical t-values. a) Why is it important to take the measurements on the same date? A. Using the same dates makes the second sample dependent on the first and reduces variability in water clarity attributable to date. B. Those are the same dates that all biologists use to take water clarity samples. C. Using the same dates makes it easier to remember to take samples. D. Using the same datos maximizes the difference in water clarity 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=-Y. Identify the null and alternative hypotheses. Hoil Hvo Determine the test statistic for this hypothesis tost. (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.) What is your conclusion regarding H,? Ho. There sufficient evidence at the a = 0,05 level of significance to conclude that the clarity of the lake is improving c) Draw a boxplot of the differenced data. Does this visual evidence support the results obtained in part (b)? ов. A Diffes Differences Oc. OD Differences Diferences Does this visual evidence support the results obtained in part (b)? A. No, because o is not contained in the boxplot. B. No, because the boxplot is too large. OC. Yes, because is contained in the boxplot. OD. Yes, because the boxplot shows no outliers.

Answer 1

1. (a) Option A

(b) Ho: $\mu$_d =0

Ha:$\mu$_d <0

t = -0.89

critical value = -2.02

fail to reject, is not

(c) Graph D

Option C

2. 45.78