Aresearcher studies water clarity at the same location in a lake on he depth (in inches) at which it is no longer visible. The collected 1 2 1/25 3/19 5/30 7/3 Observation 3 4 Date nitial Depth, X, Depth Five Years Later, Y, 9/13 65.9 74.2 60.7 66.6 69.8 73.4 73.5 65.4 70.4 76.7

MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
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Chapter1: Starting With Matlab
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In this study, a researcher investigates water clarity at a consistent location in a lake. The research involves recording measurements on identical dates over two separate years, spaced five years apart. The procedure utilizes a weighted disk painted black and white to measure the depth (in inches) at which it becomes invisible. The data collected is tabulated below:

| Observation | 1  | 2  | 3  | 4  | 5  | 6  |
|-------------|----|----|----|----|----|----|
| Date        | 1/25 | 3/19 | 5/30 | 7/3  | 9/13 | 11/7 |
| Initial Depth, \( X_i \) | 65.9 | 74.2 | 70.7 | 66.6 | 69.8 | 50.3 |
| Depth Five Years Later, \( Y_i \) | 73.4 | 73.5 | 65.4 | 70.4 | 76.7 | 52.0 |

**Tasks:**

- **a) Formulate the Null Hypothesis (\( H_0 \)) and Alternative Hypothesis (\( H_4 \)):**  
  \((Type integers or decimals. Do not round.)\)

- **b) Determine the test statistic for this hypothesis test:**  
  \((Round to two decimal places as needed.)\)

Instructions for students: Analyze the data to consider changes in water clarity over the five years, using appropriate statistical methods to test the stated hypotheses.
Transcribed Image Text:In this study, a researcher investigates water clarity at a consistent location in a lake. The research involves recording measurements on identical dates over two separate years, spaced five years apart. The procedure utilizes a weighted disk painted black and white to measure the depth (in inches) at which it becomes invisible. The data collected is tabulated below: | Observation | 1 | 2 | 3 | 4 | 5 | 6 | |-------------|----|----|----|----|----|----| | Date | 1/25 | 3/19 | 5/30 | 7/3 | 9/13 | 11/7 | | Initial Depth, \( X_i \) | 65.9 | 74.2 | 70.7 | 66.6 | 69.8 | 50.3 | | Depth Five Years Later, \( Y_i \) | 73.4 | 73.5 | 65.4 | 70.4 | 76.7 | 52.0 | **Tasks:** - **a) Formulate the Null Hypothesis (\( H_0 \)) and Alternative Hypothesis (\( H_4 \)):** \((Type integers or decimals. Do not round.)\) - **b) Determine the test statistic for this hypothesis test:** \((Round to two decimal places as needed.)\) Instructions for students: Analyze the data to consider changes in water clarity over the five years, using appropriate statistical methods to test the stated hypotheses.
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