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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 ( below Observation 1 2 3 4 5 6 1/25 3/19 5/30 7/3 9/13 11/7 71.2 35.6 53.8 41.2 57.3 43.4 72.1 35.1 59.0 41.0 61.0 47.0 Date Initial Depth, X, Depth Five Years Later, Y, Click the icon to view the table of critical t-values. COO (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. Those are the same dates that all biologists use to take water clarity samples. OC. 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.

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 ( below Observation 1 2 3 4 5 6 1/25 3/19 5/30 7/3 9/13 11/7 71.2 35.6 53.8 41.2 57.3 43.4 72.1 35.1 59.0 41.0 61.0 47.0 Date Initial Depth, X, Depth Five Years Later, Y, Click the icon to view the table of critical t-values. COO (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. Those are the same dates that all biologists use to take water clarity samples. OC. 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.

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 Date Initial Depth, X, Depth Five Years Later, Y, Click the icon to view the table of critical t-values. 4 71.2 35.6 53.8 41.2 57.3 43.4 72.1 35.1 59.0 41.0 61.0 47.0 (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. Those are the same dates that all biologists use to take water clarity samples. OC. 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.
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 Date Initial Depth, X, Depth Five Years Later, Y, Click the icon to view the table of critical t-values. 4 71.2 35.6 53.8 41.2 57.3 43.4 72.1 35.1 59.0 41.0 61.0 47.0 (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. Those are the same dates that all biologists use to take water clarity samples. OC. 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.
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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 4 5 6 1 2 3 1/25 3/19 5/30 7/3 9/13 11/7 35.6 53.8 41.2 57.3 43.4 72.1 35.1 59.0 41.0 61.0 71.2 47.0 Date Initial Depth, X₁ Depth Five Years Later, Y₁ Click the icon to view the table of critical t-values. ... (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. Those are the same dates that all biologists use to take water clarity 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 x = 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 d₁=X₁ - Y₁. Identify the null and alternative hypotheses. Ho: Hd = 0 H₁: Hd < 0 Determine the test statistic for this hypothesis test. -2.19 (Round to two decimal places as needed.) Approximate the P-value for this hypothesis test. The P-value is in the range 0 ≤ P-value < 0.001. 0.01 s P-value < 0.025. 0.025 s P-value < 0.05. 0.05 P-value <0.10. 0.10 s P-value < 0.25. 0.25 s P-value < 1. 0.005s P-value <0.01. 0.001 s P-value < 0.005.
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 4 5 6 1 2 3 1/25 3/19 5/30 7/3 9/13 11/7 35.6 53.8 41.2 57.3 43.4 72.1 35.1 59.0 41.0 61.0 71.2 47.0 Date Initial Depth, X₁ Depth Five Years Later, Y₁ Click the icon to view the table of critical t-values. ... (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. Those are the same dates that all biologists use to take water clarity 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 x = 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 d₁=X₁ - Y₁. Identify the null and alternative hypotheses. Ho: Hd = 0 H₁: Hd < 0 Determine the test statistic for this hypothesis test. -2.19 (Round to two decimal places as needed.) Approximate the P-value for this hypothesis test. The P-value is in the range 0 ≤ P-value < 0.001. 0.01 s P-value < 0.025. 0.025 s P-value < 0.05. 0.05 P-value <0.10. 0.10 s P-value < 0.25. 0.25 s P-value < 1. 0.005s P-value <0.01. 0.001 s P-value < 0.005.
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Determine the test statistic for this hypothesis test. (Round to two decimal places as needed.)
Transcribed Image Text:Determine the test statistic for this hypothesis test. (Round to two decimal places as needed.)
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Follow-up 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 1/25 3/19 5/30 7/3 9/13 11/7 71.2 35.6 53.8 41.2 57.3 43.4 72.1 35.1 59.0 41.0 61.0 47.0 Date Initial Depth, X, Depth Five Years Later, Y, Click the icon to view the table of critical t-values. (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. B. Those are the same dates that all biologists use to take water clarity samples. C. Using the same dates makes the second sample dependent on the first and reduces variability in water clarity attributable to date. 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 approximately normally distributed with no outliers. Let d = X-Y, Identify the null and alternative hypotheses. = 0 0 Ho Hd H₁: Hd 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 71.2 35.6 53.8 41.2 57.3 43.4 72.1 35.1 59.0 41.0 61.0 47.0 Date Initial Depth, X, Depth Five Years Later, Y, Click the icon to view the table of critical t-values. (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. B. Those are the same dates that all biologists use to take water clarity samples. C. Using the same dates makes the second sample dependent on the first and reduces variability in water clarity attributable to date. 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 approximately normally distributed with no outliers. Let d = X-Y, Identify the null and alternative hypotheses. = 0 0 Ho Hd H₁: Hd Determine the test statistic for this hypothesis test. (Round to two decimal places as needed.) Clear all Check answer
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Follow-up 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 3/19 5/30 7/3 9/13 11/77 1/25 71.2 35.6 53.8 41.2 57.3 43.4 72.1 35.1 59.0 41.0 61.0 47.0 Date Initial Depth, X, Depth Five Years Later, Y, Click the icon to view the table of critical t-values. (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. B. Those are the same dates that all biologists use to take water clarity samples. C. Using the same dates makes the second sample dependent on the first and reduces variability in water clarity attributable to date. 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 approximately normally distributed with no outliers. Let d, - X, - Y₁. Identify the null and alternative hypotheses. Ho: Pd H₁: Hd
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 3/19 5/30 7/3 9/13 11/77 1/25 71.2 35.6 53.8 41.2 57.3 43.4 72.1 35.1 59.0 41.0 61.0 47.0 Date Initial Depth, X, Depth Five Years Later, Y, Click the icon to view the table of critical t-values. (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. B. Those are the same dates that all biologists use to take water clarity samples. C. Using the same dates makes the second sample dependent on the first and reduces variability in water clarity attributable to date. 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 approximately normally distributed with no outliers. Let d, - X, - Y₁. Identify the null and alternative hypotheses. Ho: Pd H₁: Hd
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