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Listed below are numbers of Internet users per 100 people and numbers of scientific award winners per 10 million people for different countries. Construct a scatterplot ind the Determine whether there is sufficient evidence to support a claim of linear correlation between the two variables. Use a significance level of a =0.05. 80.6 9.1 67.3 1.6 77.8 11.1 37.6 O 0.1 Internet Users 79.5 5.6 57.5 Award Winners 3.2 ...... Construct a scatterplot. Choose the correct graph below. OA. O B. Oc. OD. 12- 12 12- 12- 04 90 30 Intermet Users 90 Intermet Uers Intamel Users Internat Uers The linear correlation coefficient is r (Round to three decimal places as needed.) Determine the null and alternative hypotheses Ho: p Hi p V (Type integers or decimals. Do not round.) The test statistio is t= (Round to two decimal places as needed.)

Listed below are numbers of Internet users per 100 people and numbers of scientific award winners per 10 million people for different countries. Construct a scatterplot ind the Determine whether there is sufficient evidence to support a claim of linear correlation between the two variables. Use a significance level of a =0.05. 80.6 9.1 67.3 1.6 77.8 11.1 37.6 O 0.1 Internet Users 79.5 5.6 57.5 Award Winners 3.2 ...... Construct a scatterplot. Choose the correct graph below. OA. O B. Oc. OD. 12- 12 12- 12- 04 90 30 Intermet Users 90 Intermet Uers Intamel Users Internat Uers The linear correlation coefficient is r (Round to three decimal places as needed.) Determine the null and alternative hypotheses Ho: p Hi p V (Type integers or decimals. Do not round.) The test statistio is t= (Round to two decimal places as needed.)

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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**Educational Website: Analyzing Correlation Between Internet Users and Scientific Award Winners** Listed below are numbers of internet users per 100 people and numbers of scientific award winners per 10 million people for different countries. Use the data to construct a scatterplot, calculate the linear correlation coefficient \( r \), and determine the P-value of \( r \). The significance level is \( \alpha = 0.05 \). | Internet Users | 79.5 | 80.6 | 57.5 | 67.3 | 77.8 | 37.6 | |----------------|------|------|------|------|------|------| | Award Winners | 5.6 | 9.1 | 3.2 | 1.6 | 11.1 | 0.1 | **Construct a Scatterplot**: Choose the correct graph below. - **Graph A**: Shows a positive relationship between the variables, but with some outliers. - **Graph B**: Shows a cluster with no apparent relationship. - **Graph C**: Displays a possible linear relationship with moderate correlation. - **Graph D**: Exhibits no apparent relationship, scattered points. **Tasks**: 1. **The Linear Correlation Coefficient**: Find and round to three decimal places. 2. **Determine Hypotheses**: - Null Hypothesis (\( H_0 \)): There is no linear correlation (\( \rho = 0 \)). - Alternative Hypothesis (\( H_1 \)): There is a linear correlation (\( \rho \neq 0 \)). 3. **The Test Statistic**: Calculate \( t \) and round to two decimal places. This exercise involves determining statistical significance between the number of internet users and scientific achievement metrics, reflecting potential relationships for demographic and educational research.
Transcribed Image Text:**Educational Website: Analyzing Correlation Between Internet Users and Scientific Award Winners** Listed below are numbers of internet users per 100 people and numbers of scientific award winners per 10 million people for different countries. Use the data to construct a scatterplot, calculate the linear correlation coefficient \( r \), and determine the P-value of \( r \). The significance level is \( \alpha = 0.05 \). | Internet Users | 79.5 | 80.6 | 57.5 | 67.3 | 77.8 | 37.6 | |----------------|------|------|------|------|------|------| | Award Winners | 5.6 | 9.1 | 3.2 | 1.6 | 11.1 | 0.1 | **Construct a Scatterplot**: Choose the correct graph below. - **Graph A**: Shows a positive relationship between the variables, but with some outliers. - **Graph B**: Shows a cluster with no apparent relationship. - **Graph C**: Displays a possible linear relationship with moderate correlation. - **Graph D**: Exhibits no apparent relationship, scattered points. **Tasks**: 1. **The Linear Correlation Coefficient**: Find and round to three decimal places. 2. **Determine Hypotheses**: - Null Hypothesis (\( H_0 \)): There is no linear correlation (\( \rho = 0 \)). - Alternative Hypothesis (\( H_1 \)): There is a linear correlation (\( \rho \neq 0 \)). 3. **The Test Statistic**: Calculate \( t \) and round to two decimal places. This exercise involves determining statistical significance between the number of internet users and scientific achievement metrics, reflecting potential relationships for demographic and educational research.
**Data Analysis and Correlation Test** Listed below are the numbers of Internet users per 100 people and numbers of scientific award winners per 10 million people for different countries. The task is to construct a scatterplot, find the value of the linear correlation coefficient \( r \), and determine the P-value of \( r \). We'll assess whether there is sufficient evidence to support a claim of linear correlation between these two variables using a significance level of \( \alpha = 0.05 \). **Data:** - **Internet Users:** 79.5, 80.6, 57.5, 67.3, 77.8, 37.6 - **Award Winners:** 5.6, 9.1, 3.2, 1.6, 11.1, 0.1 **Scatterplots Analysis:** - Four different scatterplots are displayed, each with Internet Users on the x-axis and Award Winners on the y-axis. - Each scatterplot displays a set of data points corresponding to the given data values. **Linear Correlation Coefficient \( r \):** - A blank space is provided to calculate and fill in the linear correlation coefficient \( r \), which should be rounded to three decimal places. **Hypotheses:** - **Null Hypothesis \( H_0 \):** - \( \rho = 0 \) (There is no linear correlation between the two variables.) - **Alternative Hypothesis \( H_1 \):** - \( \rho \neq 0 \) (There is a linear correlation between the two variables.) **Test Statistic and P-value:** - Spaces are provided for entry of: - The test statistic \( t \) (rounded to two decimal places). - The P-value of \( r \) (rounded to three decimal places). **Conclusion:** - Depending on the P-value, determine whether it is less than or greater than the significance level: - If the P-value is less than the significance level, reject the null hypothesis. - Otherwise, do not reject the null hypothesis. - A dropdown allows for the selection of "sufficient" or "insufficient" evidence to support the claim of a linear correlation. This exercise will help understand the relationship between the number of internet users and scientific award winners across different countries.
Transcribed Image Text:**Data Analysis and Correlation Test** Listed below are the numbers of Internet users per 100 people and numbers of scientific award winners per 10 million people for different countries. The task is to construct a scatterplot, find the value of the linear correlation coefficient \( r \), and determine the P-value of \( r \). We'll assess whether there is sufficient evidence to support a claim of linear correlation between these two variables using a significance level of \( \alpha = 0.05 \). **Data:** - **Internet Users:** 79.5, 80.6, 57.5, 67.3, 77.8, 37.6 - **Award Winners:** 5.6, 9.1, 3.2, 1.6, 11.1, 0.1 **Scatterplots Analysis:** - Four different scatterplots are displayed, each with Internet Users on the x-axis and Award Winners on the y-axis. - Each scatterplot displays a set of data points corresponding to the given data values. **Linear Correlation Coefficient \( r \):** - A blank space is provided to calculate and fill in the linear correlation coefficient \( r \), which should be rounded to three decimal places. **Hypotheses:** - **Null Hypothesis \( H_0 \):** - \( \rho = 0 \) (There is no linear correlation between the two variables.) - **Alternative Hypothesis \( H_1 \):** - \( \rho \neq 0 \) (There is a linear correlation between the two variables.) **Test Statistic and P-value:** - Spaces are provided for entry of: - The test statistic \( t \) (rounded to two decimal places). - The P-value of \( r \) (rounded to three decimal places). **Conclusion:** - Depending on the P-value, determine whether it is less than or greater than the significance level: - If the P-value is less than the significance level, reject the null hypothesis. - Otherwise, do not reject the null hypothesis. - A dropdown allows for the selection of "sufficient" or "insufficient" evidence to support the claim of a linear correlation. This exercise will help understand the relationship between the number of internet users and scientific award winners across different countries.
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