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The data below are ages and systolic blood pressures (measured in millimeters of mercury) of 9 randomly selected adults.   a)Identify the null and alternative hypotheses b)Find the linear correlation coefficient. Round the answer to 3 decimal places. c)Find the test statistics d)Find the p-value andcritical value e)Reject H0" or "Do not reject H0"? f)State the conclusion. g)Find the equation of the regression line for the given data. Round the regression line values to 2 decimal places. h)What would be the predicted pressure if the age was 60? Round the predicted pressure to the nearest whole number.

The data below are ages and systolic blood pressures (measured in millimeters of mercury) of 9 randomly selected adults.   a)Identify the null and alternative hypotheses b)Find the linear correlation coefficient. Round the answer to 3 decimal places. c)Find the test statistics d)Find the p-value andcritical value e)Reject H0" or "Do not reject H0"? f)State the conclusion. g)Find the equation of the regression line for the given data. Round the regression line values to 2 decimal places. h)What would be the predicted pressure if the age was 60? Round the predicted pressure to the nearest whole number.

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)
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ISBN:9781337111348
Author:Bruce Crauder, Benny Evans, Alan Noell
Publisher:Bruce Crauder, Benny Evans, Alan Noell
Chapter3: Straight Lines And Linear Functions
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The data below are ages and systolic blood pressures (measured in millimeters of mercury) of 9 randomly selected adults.

 

a)Identify the null and alternative hypotheses

b)Find the linear correlation coefficient. Round the answer to 3 decimal places.

c)Find the test statistics

d)Find the p-value andcritical value

e)Reject H0" or "Do not reject H0"?

f)State the conclusion.

g)Find the equation of the regression line for the given data. Round the regression line values to 2 decimal places.

h)What would be the predicted pressure if the age was 60? Round the predicted pressure to the nearest whole number.

### Analyzing the Correlation Between Age and Systolic Blood Pressure In this educational example, we will examine the linear correlation between age (denoted as \( x \)) and systolic blood pressure (denoted as \( y \)) at a significance level of \( \alpha = 0.05 \). #### Provided Data: | Age, \( x \) | 39 | 41 | 45 | 48 | 51 | 53 | 57 | 61 | 65 | |--------------|----|----|----|----|----|----|----|----|----| | Pressure, \( y \) | 115 | 120 | 123 | 131 | 142 | 145 | 148 | 150 | 152 | #### Objective: To determine whether there is a statistically significant linear correlation between the variables age and systolic blood pressure at the \( \alpha = 0.05 \) significance level. #### Steps to Determine Linear Correlation: 1. **Plot the Data**: Create a scatter plot with 'Age' on the x-axis and 'Systolic Blood Pressure' on the y-axis to visually assess the relationship. 2. **Calculate the Correlation Coefficient** \( r \): Use the formula for Pearson's correlation coefficient to quantify the strength and direction of the linear relationship between the two variables. 3. **Test the Significance of the Correlation Coefficient**: - Null Hypothesis (\( H_0 \)): There is no linear correlation between age and systolic blood pressure (\( \rho = 0 \)). - Alternative Hypothesis (\( H_1 \)): There is a linear correlation between age and systolic blood pressure (\( \rho \neq 0 \)). 4. **Determine the Critical Value**: Check the critical value for the correlation coefficient based on the given \( \alpha \) level and degrees of freedom (\( df = n - 2 \)) where \( n \) is the number of pairs. 5. **Compare the Computed \( r \) Value**: If the computed \( r \) value is greater than the critical value, reject the null hypothesis. 6. **Conclusion**: Based on the comparison, conclude whether there is a significant linear correlation between age and systolic blood pressure. This process allows us to scientifically determine if age is a predictor of systolic blood pressure, which can be crucial for
Transcribed Image Text:### Analyzing the Correlation Between Age and Systolic Blood Pressure In this educational example, we will examine the linear correlation between age (denoted as \( x \)) and systolic blood pressure (denoted as \( y \)) at a significance level of \( \alpha = 0.05 \). #### Provided Data: | Age, \( x \) | 39 | 41 | 45 | 48 | 51 | 53 | 57 | 61 | 65 | |--------------|----|----|----|----|----|----|----|----|----| | Pressure, \( y \) | 115 | 120 | 123 | 131 | 142 | 145 | 148 | 150 | 152 | #### Objective: To determine whether there is a statistically significant linear correlation between the variables age and systolic blood pressure at the \( \alpha = 0.05 \) significance level. #### Steps to Determine Linear Correlation: 1. **Plot the Data**: Create a scatter plot with 'Age' on the x-axis and 'Systolic Blood Pressure' on the y-axis to visually assess the relationship. 2. **Calculate the Correlation Coefficient** \( r \): Use the formula for Pearson's correlation coefficient to quantify the strength and direction of the linear relationship between the two variables. 3. **Test the Significance of the Correlation Coefficient**: - Null Hypothesis (\( H_0 \)): There is no linear correlation between age and systolic blood pressure (\( \rho = 0 \)). - Alternative Hypothesis (\( H_1 \)): There is a linear correlation between age and systolic blood pressure (\( \rho \neq 0 \)). 4. **Determine the Critical Value**: Check the critical value for the correlation coefficient based on the given \( \alpha \) level and degrees of freedom (\( df = n - 2 \)) where \( n \) is the number of pairs. 5. **Compare the Computed \( r \) Value**: If the computed \( r \) value is greater than the critical value, reject the null hypothesis. 6. **Conclusion**: Based on the comparison, conclude whether there is a significant linear correlation between age and systolic blood pressure. This process allows us to scientifically determine if age is a predictor of systolic blood pressure, which can be crucial for
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