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 weighteddisk 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.Observation123456Date1/25 3/19 5/307/39/13 11/7Initial Depth, X;37.2 43.4 47.7 67.2 49.7 53.3Depth Five Years Later, Y;44.443.2 52.4 71.0 55.9 55.4a) Why is it important to take the measurements on the same date?O A. Using the same dates makes it easier to remember to take samples.eO B. Using the same dates makes the second sample dependent on the first and reduces variability in water clarity attributable to date.O C. Those are the same dates that all biologists use to take water clarity samplesO D. 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 plot and boxplot of the data indicate that the differences are approximatelynormally distributed with no outliers.Let d, = X, - Y;. Identify the null and alternative hypotheses.Determine the test statistic for this hypothesis test. O (Round to two decimal places as needed.)НоFind the P-value for this hypothesis test. P-value =(Round to three decimal places as needed.)H,:(Type integers or decimals. Do not round.)Vhat is your conclusion regarding H,?O A. Do not reject Hn. There is not sufficient evidence at the a= 0.05 level of significance to conclude that the clarity of the lake is improving.O B. Reject Hg. There is sufficient evidence at the a = 0.05 level of significance to conclude that the clarity of the lake is improving.O C. Do not reject Hn. There is sufficient evidence at the a= 0.05 level of significance to conclude that the clarity of the lake is improving.O D. Reject H,. There is not sufficient evidence at the a= 0.05 level of significance to conclude that the clarity of the lake is improving.:) Draw a boxplot of the differenced data. Does this visual evidence support the results obtained in part b)?Choose the correct graph below.DA.OB.OC.OD.QQDifferenceDifferenceDifferenceDifferenceDoes this visual evidence support the results obtained in part b)?O A. Yes because the boxplot supports that the lake is becoming more clear, since most differences are positive or near 0.O B. Yes because the boxplot supports that the lake is becoming more clear, since most differences are negative.O C. No because the boxplot supports that the lake is not becoming more clear, since most differences are positive or near 0.O D. No because the boxplot supports that the lake is not becoming more clear, since most differences are negative.?

a) The suitable test for above example is paired t test. and in the paired t test we study the…

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 isk 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 nitial Depth, X, 1 2 3 4 1/25 3/19 5/30 713 9/13 11/7 37.2 43.4 47.7 67.2 49.7 53.3 Depth Five Years Later, Y; 44.4 43.2 52.4 71.0 55.9 55.4

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 isk 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 nitial Depth, X, 1 2 3 4 1/25 3/19 5/30 713 9/13 11/7 37.2 43.4 47.7 67.2 49.7 53.3 Depth Five Years Later, Y; 44.4 43.2 52.4 71.0 55.9 55.4

Holt Mcdougal Larson Pre-algebra: Student Edition 2012

1st Edition

ISBN:9780547587776

Author:HOLT MCDOUGAL

Publisher:HOLT MCDOUGAL

Chapter1: Variables, Expressions, And Integers

Section1.5: Adding Integers

Problem 45E

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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 1/25 3/19 5/30 7/3 9/13 11/7 41.6 72.7 72.4 65.9 64.2 68.6 49.3 72.1 76.6 69.4 69.8 70.5 Date Initial Depth, X, Depth Five Years Later, Y, a) Why is it important to take the measurements on the same date? CA. Using the same dates makes it easier to remember to take samples. B. Using the same dates maximizes the difference in water clarity. OC. Those are the same dates that all biologists use to take water clarity samples. D. 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…
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