SALIVA COTININE LEVELS: In a study of saliva cotinine, seven subjects, all of whom had abstained from smoking for a week, were asked to smoke a single cigarette. The cotinine levels at 12 hours (X) and 24 hours (Y) after smoking are provided

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# Saliva Cotinine Levels Study

## Overview
A study was conducted to examine saliva cotinine levels in seven subjects who abstained from smoking for a week. Each subject smoked a single cigarette, and their cotinine levels were measured at 12 hours (X) and 24 hours (Y) post-smoking.

## Data
The cotinine levels for each subject are as follows:

| Subject | After 12 hr (X) | After 24 hr (Y) |
|---------|-----------------|-----------------|
| 1       | 73              | 24              |
| 2       | 58              | 27              |
| 3       | 66              | 30              |
| 4       | 93              | 59              |
| 5       | 33              | 0               |
| 6       | 18              | 11              |
| 7       | 147             | 49              |

## Steps for Analysis
1. **Assumption**: It is logical to explore a relationship between the 12-hour and 24-hour cotinine levels.

2. **Scatter Plot**: Construct a scatter plot of the variables X (12-hour levels) and Y (24-hour levels) to observe any correlations.

3. **Hypotheses**
   - **Null Hypothesis (\(H_0\))**: There is no correlation (\(\rho = 0\)).
   - **Alternative Hypothesis (\(H_1\))**: There is a non-zero correlation (\(\rho \neq 0\)).
   
4. **Correlation Calculation**: Calculate the correlation coefficient (r) for the variables.

5. **Statistical Significance**: Determine the statistical significance of the correlation:
   - Not significant at \(\alpha = 0.05\) and \(\alpha = 0.01\).

6. **Regression Equation**: Develop a regression equation for the data: \(Y =\)

7. **Prediction**: Estimate the cotinine level at 24 hours when the 12-hour level is 69.86 mmol/L. 

This exercise allows for practical application of statistical concepts such as correlation and regression in assessing changes in biochemical markers following exposure to smoking.
Transcribed Image Text:# Saliva Cotinine Levels Study ## Overview A study was conducted to examine saliva cotinine levels in seven subjects who abstained from smoking for a week. Each subject smoked a single cigarette, and their cotinine levels were measured at 12 hours (X) and 24 hours (Y) post-smoking. ## Data The cotinine levels for each subject are as follows: | Subject | After 12 hr (X) | After 24 hr (Y) | |---------|-----------------|-----------------| | 1 | 73 | 24 | | 2 | 58 | 27 | | 3 | 66 | 30 | | 4 | 93 | 59 | | 5 | 33 | 0 | | 6 | 18 | 11 | | 7 | 147 | 49 | ## Steps for Analysis 1. **Assumption**: It is logical to explore a relationship between the 12-hour and 24-hour cotinine levels. 2. **Scatter Plot**: Construct a scatter plot of the variables X (12-hour levels) and Y (24-hour levels) to observe any correlations. 3. **Hypotheses** - **Null Hypothesis (\(H_0\))**: There is no correlation (\(\rho = 0\)). - **Alternative Hypothesis (\(H_1\))**: There is a non-zero correlation (\(\rho \neq 0\)). 4. **Correlation Calculation**: Calculate the correlation coefficient (r) for the variables. 5. **Statistical Significance**: Determine the statistical significance of the correlation: - Not significant at \(\alpha = 0.05\) and \(\alpha = 0.01\). 6. **Regression Equation**: Develop a regression equation for the data: \(Y =\) 7. **Prediction**: Estimate the cotinine level at 24 hours when the 12-hour level is 69.86 mmol/L. This exercise allows for practical application of statistical concepts such as correlation and regression in assessing changes in biochemical markers following exposure to smoking.
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