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usband. Find the best predicted value of y given that the husband has an IQ of 100? Use a significance level of 0.05. E Click the icon to view the critical values of the Pearson correlation coefficient r. The best predicted value of y is Round to two decimal places as needed.)

usband. Find the best predicted value of y given that the husband has an IQ of 100? Use a significance level of 0.05. E Click the icon to view the critical values of the Pearson correlation coefficient r. The best predicted value of y is 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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**Critical Values of the Pearson Correlation Coefficient (r)** This table provides the critical values for the Pearson Correlation Coefficient (r) at significance levels \(\alpha = 0.05\) and \(\alpha = 0.01\). It is used to determine whether the correlation between two variables is statistically significant. **Table Explanation:** - **Columns:** - **n**: Represents the sample size. - \(\alpha = 0.05\): Critical value when using a 5% significance level. - \(\alpha = 0.01\): Critical value when using a 1% significance level. - **Rows:** - Each row corresponds to a different sample size (n), ranging from 4 to 50. **Usage:** - To test the null hypothesis \(H_0: \rho = 0\) against the alternative hypothesis \(H_1: \rho \neq 0\). - Reject \(H_0\) if the absolute value of the observed correlation coefficient (r) is greater than the critical value provided in the table. **Sample Values:** - For \(n = 4\): - \(\alpha = 0.05\): Critical value is 0.950 - \(\alpha = 0.01\): Critical value is 0.990 - For \(n = 5\): - \(\alpha = 0.05\): Critical value is 0.878 - \(\alpha = 0.01\): Critical value is 0.959 - For \(n = 50\): - \(\alpha = 0.05\): Critical value is 0.279 - \(\alpha = 0.01\): Critical value is 0.361 This table is essential for determining the statistical significance of a correlation in a data sample, assisting researchers and students in making inferences about the relationships between variables.
Transcribed Image Text:**Critical Values of the Pearson Correlation Coefficient (r)** This table provides the critical values for the Pearson Correlation Coefficient (r) at significance levels \(\alpha = 0.05\) and \(\alpha = 0.01\). It is used to determine whether the correlation between two variables is statistically significant. **Table Explanation:** - **Columns:** - **n**: Represents the sample size. - \(\alpha = 0.05\): Critical value when using a 5% significance level. - \(\alpha = 0.01\): Critical value when using a 1% significance level. - **Rows:** - Each row corresponds to a different sample size (n), ranging from 4 to 50. **Usage:** - To test the null hypothesis \(H_0: \rho = 0\) against the alternative hypothesis \(H_1: \rho \neq 0\). - Reject \(H_0\) if the absolute value of the observed correlation coefficient (r) is greater than the critical value provided in the table. **Sample Values:** - For \(n = 4\): - \(\alpha = 0.05\): Critical value is 0.950 - \(\alpha = 0.01\): Critical value is 0.990 - For \(n = 5\): - \(\alpha = 0.05\): Critical value is 0.878 - \(\alpha = 0.01\): Critical value is 0.959 - For \(n = 50\): - \(\alpha = 0.05\): Critical value is 0.279 - \(\alpha = 0.01\): Critical value is 0.361 This table is essential for determining the statistical significance of a correlation in a data sample, assisting researchers and students in making inferences about the relationships between variables.
Suppose IQ scores were obtained for 20 randomly selected sets of couples. The 20 pairs of measurements yield \(\bar{x} = 99.48\), \(\bar{y} = 99.05\), \(r = 0.894\), \(P\text{-value} = 0.000\), and \(\hat{y} = 21.13 + 0.78x\), where \(x\) represents the IQ score of the husband. Find the best predicted value of \(\hat{y}\) given that the husband has an IQ of 100? Use a significance level of 0.05. [Click the icon to view the critical values of the Pearson correlation coefficient \(r\).] The best predicted value of \(\hat{y}\) is [ ]. (Round to two decimal places as needed.)
Transcribed Image Text:Suppose IQ scores were obtained for 20 randomly selected sets of couples. The 20 pairs of measurements yield \(\bar{x} = 99.48\), \(\bar{y} = 99.05\), \(r = 0.894\), \(P\text{-value} = 0.000\), and \(\hat{y} = 21.13 + 0.78x\), where \(x\) represents the IQ score of the husband. Find the best predicted value of \(\hat{y}\) given that the husband has an IQ of 100? Use a significance level of 0.05. [Click the icon to view the critical values of the Pearson correlation coefficient \(r\).] The best predicted value of \(\hat{y}\) is [ ]. (Round to two decimal places as needed.)
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The p-value is 0.000.

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