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The accompanying table lists the ages of acting award winners matched by the years in which the awards were won. Construct a scatterplot, find the value of the linear correlation coefficient r, and find the P-value of r. Determine whether there is sufficient evidence to support a claim of linear correlation between the two variables. Should we expect that there would be a correlation? Use a significance level of a = 0.01.

The accompanying table lists the ages of acting award winners matched by the years in which the awards were won. Construct a scatterplot, find the value of the linear correlation coefficient r, and find the P-value of r. Determine whether there is sufficient evidence to support a claim of linear correlation between the two variables. Should we expect that there would be a correlation? Use a significance level of a = 0.01.

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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3- Hi wonderful Bartleby Team, I am struggling with this chapter in general, Please provide answers and a short explanations for all the parts of the exercise. Thaks in advance.

The accompanying table lists the ages of acting award winners matched by the years in which the awards were won. You are tasked with constructing a scatterplot, finding the value of the linear correlation coefficient \( r \), and determining the P-value of \( r \). The goal is to assess whether there is sufficient evidence to support a claim of linear correlation between the two variables—age of Best Actress and Best Actor at the time of their award. A significance level of \(\alpha = 0.01\) is used. ### Steps to Analyze the Data: 1. **Construct a Scatterplot:** - The scatterplot helps visualize the relationship between the ages of Best Actresses and Best Actors. Look for the plot where the data points seem to follow a straight line (positive or negative correlation). 2. **Linear Correlation Coefficient \( r \):** - Calculate \( r \) to quantify the direction and strength of the linear relationship. - Provide the value rounded to three decimal places. 3. **Hypotheses:** - **Null Hypothesis \( H_0 \):** There is no linear correlation (\( \rho = 0 \)). - **Alternative Hypothesis \( H_1 \):** There is a linear correlation (\( \rho \neq 0 \)). 4. **Test Statistic and P-value:** - Calculate the test statistic \( t \) and round it to two decimal places. - Determine the P-value and round it to three decimal places. ### Data Table: The data presents the ages of Best Actresses and Best Actors at the time they received their awards: | Age (Years) | Best Actress | 28 | 30 | 33 | 32 | 36 | 40 | 51 | 62 | 42 | 54 | | ----------- | ------------- | | Best Actor | 42 | 39 | 37 | 47 | 55 | 49 | 62 | 45 | 35 | 34 | ### Diagram Explanation: - **Graphs A to D:** Each graph is a scatterplot with "Best Actress (years)" on the x-axis and "Best Actor (years)" on the y-axis. The challenge is to match the correct scatterplot that reflects the age data from the table above. Data clustering close to a line indicates correlation. This analysis helps determine if there is a pattern of correlation between the ages of winners of
Transcribed Image Text:The accompanying table lists the ages of acting award winners matched by the years in which the awards were won. You are tasked with constructing a scatterplot, finding the value of the linear correlation coefficient \( r \), and determining the P-value of \( r \). The goal is to assess whether there is sufficient evidence to support a claim of linear correlation between the two variables—age of Best Actress and Best Actor at the time of their award. A significance level of \(\alpha = 0.01\) is used. ### Steps to Analyze the Data: 1. **Construct a Scatterplot:** - The scatterplot helps visualize the relationship between the ages of Best Actresses and Best Actors. Look for the plot where the data points seem to follow a straight line (positive or negative correlation). 2. **Linear Correlation Coefficient \( r \):** - Calculate \( r \) to quantify the direction and strength of the linear relationship. - Provide the value rounded to three decimal places. 3. **Hypotheses:** - **Null Hypothesis \( H_0 \):** There is no linear correlation (\( \rho = 0 \)). - **Alternative Hypothesis \( H_1 \):** There is a linear correlation (\( \rho \neq 0 \)). 4. **Test Statistic and P-value:** - Calculate the test statistic \( t \) and round it to two decimal places. - Determine the P-value and round it to three decimal places. ### Data Table: The data presents the ages of Best Actresses and Best Actors at the time they received their awards: | Age (Years) | Best Actress | 28 | 30 | 33 | 32 | 36 | 40 | 51 | 62 | 42 | 54 | | ----------- | ------------- | | Best Actor | 42 | 39 | 37 | 47 | 55 | 49 | 62 | 45 | 35 | 34 | ### Diagram Explanation: - **Graphs A to D:** Each graph is a scatterplot with "Best Actress (years)" on the x-axis and "Best Actor (years)" on the y-axis. The challenge is to match the correct scatterplot that reflects the age data from the table above. Data clustering close to a line indicates correlation. This analysis helps determine if there is a pattern of correlation between the ages of winners of
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