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 Date 1/253/195/307/39/13 11/7 Initial Depth, X 37.5 70.3 36.2 52.7 395 62.4 Depth Five Years Later, Y 418 69.4 44.350.8 426 58.8 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. Those are the same dates that all biologists use to take water clarity samples. B. Using the same dates makes it easier to remember to take samples. c. Using the same dates makes the second sample dependent on the first and reduces variability in water clarity attributable to date OD. Using the same dates 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 piot and boxplot of the data indicate that the differences are approximately normally distributed with no outliers. Let d. - X - Y, Identify the null and alternative hypotheses. Hoid Determine the test statistic for this hypothesis test. (Round to two decimal places as needed.) Find the critical value(8) for this hypothesis test. (Use a comma to separate answers as needed. Round to two decimal places as needed.) What is your conclusion regarding Hy? 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]? A OB -10-8 Differences Derences Ос. Differences Denonces Does this visual evidence support the results obtained in part (b)? Yes, because O is contained in the boxpilot. B. No, because the boxplot is too large OC. No, because o is not contained in the boxplot. OD. Yes, because the boxplot shows no outiers.

Answer 1

a)

OC. Using the same dates makes the second sample dependent on the first and reduces variability in water clarity attributable to date.

b)

null Hypothesis:μd		=	0
alternate Hypothesis: μd		<	0

S. No	X	Y	diff:(d)=x1-x2	d2
1	37.5	41.8	-4.3	18.49
2	70.3	69.4	0.9	0.81
3	36.2	44.3	-8.1	65.61
4	52.7	50.8	1.9	3.61
5	39.5	42.6	-3.1	9.61
6	62.4	58.8	3.6	12.96
	total	=	Σd=-9.1	Σd2=111.09
	mean dbar=	d̅     =	-1.5167
	degree of freedom =n-1                            =		5
	Std deviaiton SD=√(Σd2-(Σd)2/n)/(n-1) =		4.411085
	std error=Se=SD/√n=		1.8008
	test statistic            =	(d̅-μd)/Se         =	-0.84

critical value = -2.02

fail to reject Ho ; there is not sufficient evidence,,,,,,,,,,

c)

OA. 108 10 다 Drences

O A. Yes, because is contained in the boxplot.