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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 of the same 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 1/25 3/19 5/30 7/3 9/13 4 5 6 11/7 72.4 65.9 64.2 68.6 41.6 72.7 49.3 721 76.6 69.4 69.8 70.5 Date Initial Depth, X, Depth Five Years Later, Y, 72.7 724 a) Why is it important to take the measurements on the same date? OA. Using the same dates makes it easier to remember to take samples. OB. 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 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-Y, Identify the null and alternative hypotheses. 4 Ho Hd = 0 <0 H₁ Ha (Type integers or decimals. Do not round) Determine the test statistic for this hypothesis test (Round to two decimal places as needed)

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 of the same 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 1/25 3/19 5/30 7/3 9/13 4 5 6 11/7 72.4 65.9 64.2 68.6 41.6 72.7 49.3 721 76.6 69.4 69.8 70.5 Date Initial Depth, X, Depth Five Years Later, Y, 72.7 724 a) Why is it important to take the measurements on the same date? OA. Using the same dates makes it easier to remember to take samples. OB. 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 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-Y, Identify the null and alternative hypotheses. 4 Ho Hd = 0 <0 H₁ Ha (Type integers or decimals. Do not round) Determine the test statistic for this hypothesis test (Round to two decimal places as needed)

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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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 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-Y, Identify the null and alternative hypotheses. D Ho: Ha 0 H₁: Pd < 0 (Type integers or decimals. Do not round.) Determine the test statistic for this hypothesis test. (Round to two decimal places as needed.) Clear all Check answer
Transcribed Image Text: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 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-Y, Identify the null and alternative hypotheses. D Ho: Ha 0 H₁: Pd < 0 (Type integers or decimals. Do not round.) Determine the test statistic for this hypothesis test. (Round to two decimal places as needed.) Clear all Check answer
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**Determine the test statistic for this hypothesis test.** *(Round to two decimal places as needed.)* (Note: There are no graphs or diagrams present in this image.)
Transcribed Image Text:**Determine the test statistic for this hypothesis test.** *(Round to two decimal places as needed.)* (Note: There are no graphs or diagrams present in this image.)
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