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 4 5 6 Date ​1/25 ​3/19 ​5/30 ​7/3 ​9/13 ​11/7 Initial​ Depth, Xi 74.5 58.5 40.6 72.4 67.8 52.5 Depth Five Years​ Later, Yi 73.0 57.6 36.8 73.5 63.5 54.7 ​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. Using the same dates maximizes the difference in water clarity. C. Those are the same dates that all biologists use to take water clarity samples. D. Using the same dates makes it easier to remember to take samples. ​b) Does the evidence suggest that the clarity of the lake is improving at the alpha equals 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 diequalsXiminusYi. Identify the null and alternative hypotheses. Upper H 0​: ▼ p sigma Subscript d mu Subscript d ▼ not equals less than equals greater than nothing Upper H 1​: ▼ mu Subscript d p sigma Subscript d ▼ equals less than greater than not equals nothing ​(Type integers or decimals. Do not​ round.) Determine the test statistic for this hypothesis test. nothing ​(Round to two decimal places as​ needed.) Find the​ P-value for this hypothesis test. ​P-valueequals nothing ​(Round to three decimal places as​ needed.) What is your conclusion regarding Upper H 0​? A. Do not reject Upper H 0. There is sufficient evidence at the alphaequals0.05 level of significance to conclude that the clarity of the lake is improving. B. Reject Upper H 0. There is sufficient evidence at the alphaequals0.05 level of significance to conclude that the clarity of the lake is improving. C. Do not reject Upper H 0. There is not sufficient evidence at the alphaequals0.05 level of significance to conclude that the clarity of the lake is improving. D. Reject Upper H 0. There is not sufficient evidence at the alphaequals0.05 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)? Choose the correct graph below. A. 0 -3 6 Difference A boxplot has a horizontal axis labeled Differences from negative 3 to 6 in increments of 1. Vertical line segments are drawn at the following values: negative 1.1, 1.2, 3.8. A box encloses the vertical line segments. Horizontal line segments extend outward from both sides of the box to the plotted points at minus 2.2 and 4.3. All values are approximate. B. 0 -3 6 Difference A boxplot has a horizontal axis labeled Differences from negative 3 to 6 in increments of 1. Vertical line segments are drawn at the following values: negative 1.1, 0.4, 1.8. A box encloses the vertical line segments. Horizontal line segments extend outward from both sides of the box to the plotted points at minus 2.2 and 2.3. All values are approximate. C. 0 -3 6 Difference A boxplot has a horizontal axis labeled Differences from negative 3 to 6 in increments of 1. Vertical line segments are drawn at the following values: negative 0.1, 2.2, 4.8. A box encloses the vertical line segments. Horizontal line segments extend outward from both sides of the box to the plotted points at minus 1.2 and 5.3. All values are approximate. D. 0 -3 6 Difference A boxplot has a horizontal axis labeled Differences from negative 3 to 6 in increments of 1. Vertical line segments are drawn at the following values: negative 0.1, 1.4, 2.8. A box encloses the vertical line segments. Horizontal line segments extend outward from both sides of the box to the plotted points at minus 1.2 and 3.3. All values are approximate. Does this visual evidence support the results obtained in part​ b)? A. No because the boxplot supports that the lake is becoming more​ clear, since most differences are positive or near 0. B. Yes because the boxplot supports that the lake is not becoming more​ clear, since most differences are positive or near 0. C. No because the boxplot supports that the lake is becoming more​ clear, since most differences are negative. D. Yes because the boxplot supports that the lake is not becoming more​ clear, since most differences are negative. Click to select your answer(s).

Answer 1

The box plot is represented below

Case Processing Summary
	Cases
	Valid		Missing		Total
	N	Percent	N	Percent	N	Percent
X	6	100.0%	0	0.0%	6	100.0%
Y	6	100.0%	0	0.0%	6	100.0%

Yes, the visual evidence support the results obtained in part b, because the boxplot supports that the lake is not becoming more clear since most difference are positive or near 0.