**Hours Studied and Test Grades**The following table shows the hours studied and corresponding test grade earned by students on a recent test. Calculate the correlation coefficient, \(r\), and determine whether \(r\) is statistically significant at the 0.01 level of significance. Round your answer to the nearest thousandth.**Critical Values of the Pearson Correlation Coefficient**| Hours Studied and Test Grades ||-------------------------------|| **Hours Studied** | 0 | 0.5 | 1 | 1 | 2 | 2.25 | 3.25 | 3.5 | 3.75 | 3.75 | 4 | 5 || **Test Grade** | 72 | 64 | 68 | 81 | 79 | 85 | 82 | 72 | 99 | 87 | 84 | 97 | ### Statistical Significance of Pearson's Correlation Coefficient#### Determine the Significance of \[ r \]\[ r = \_\_\_\_\_\_\_\_\_ \]Is \[ r \] statistically significant at the 0.01 level of significance?**Instructions:**1. **Enter the value of \[ r \]**: Input the calculated Pearson's correlation coefficient value in the provided space.2. **Evaluate Significance**: Use statistical tables or software to determine if the value of \[ r \] is significant at the 0.01 level. The significance indicates how likely it is that the observed correlation is due to chance.**Step-by-Step Guide:**1. **Compute the Pearson's correlation coefficient (\[ r \])** using appropriate data.2. **Refer to the critical value table**: For a given degree of freedom \[ n-2 \], where \[ n \] is the sample size, find the critical value corresponding to the 0.01 significance level.3. **Compare \[ r \] value**: Check if the absolute value of \[ r \] is greater than the critical value from the table. If it is, then \[ r \] is statistically significant at the 0.01 level.**Concept Explanation:**- **Pearson's correlation coefficient (\[ r \])** measures the strength and direction of the linear relationship between two variables.- **Statistical significance** at the 0.01 level means there is only a 1% chance that the observed correlation occurred randomly, implying a 99% confidence level.**Further Reading:**- [Pearson Correlation Coefficient](https://en.wikipedia.org/wiki/Pearson_correlation_coefficient)- [Significance Testing](https://en.wikipedia.org/wiki/Statistical_significance)---This content helps you understand how to determine the statistical significance of a correlation coefficient in your data analysis, ensuring accurate and reliable results.

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Answered: The following table shows the hours…

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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The output below shows the relationship between stress and job performance: Correlation Stress Job performance Stress Pearson Correlation 1 Sig. (2-tailed) N 213 Job performance Pearson Correlation -.682** 1 Sig. (2-tailed) .000 N 213 213 **. Correlation is significant at the 0.01 level (2-tailed). Question: The correlation output shows what type of relationship?
What is the relationship between the number of minutes per day a woman spends talking on the phone and the woman's weight? The time on the phone and weight for 7 women are shown in the table below. Time Pounds 41 32 90 32 31 33 82 131 112 144 104 113 120 142 a. Find the correlation coefficient: r = b. The null and alternative hypotheses for correlation are: Ho: ? = 0 H₁: ?0 The p-value is: Round to 2 decimal places. (Round to four decimal places) c. Use a level of significance of a = 0.05 to state the conclusion of the hypothesis test in the context of the study. There is statistically insignificant evidence to conclude that there is a correlation between the time women spend on the phone and their weight. Thus, the use of the regression line is not appropriate. O There is statistically insignificant evidence to conclude that a woman who spends more time on the phone will weigh more than a woman who spends less time on the phone. O There is statistically significant evidence to…
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