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Suppose IQ scores were obtained for 20 randomly selected sets of siblings. The 20 pairs of measurements yield x= 99.49, y= 100.1, r=0.884, P-value = 0.000, and y = 6.29 +0.94x, where x represents the IQ score of the alue of y given that the younger child has an IQ of 104? Use a significance level of 0.05. 9 Click the icon to view the critical values of the Pearson correlation coefficient r. Critical Values of the Pearson Correlation Coefficient r he best predicted value of y is Round to two decimal places as needed.) Critical Values of the Pearson Correlation Coefficient r NOTE: To test H,: p=0 Jagainst H,: pz0, reject H, f the absolute value of r is greater than the critical value in the table. a =0.05 0.950 n a= 0.01 0.990 0.878 0.959 6 0.811 0.917 7 0.754 0.875 8 0.707 0.834 0.666 0.632 0.602 9 0.798 0.765 0.735 10 11 12 13 14 0.576 0.708 0.684 0.661 0.553 0.532 15 0.514 0.641 16 0.497 0623

Suppose IQ scores were obtained for 20 randomly selected sets of siblings. The 20 pairs of measurements yield x= 99.49, y= 100.1, r=0.884, P-value = 0.000, and y = 6.29 +0.94x, where x represents the IQ score of the alue of y given that the younger child has an IQ of 104? Use a significance level of 0.05. 9 Click the icon to view the critical values of the Pearson correlation coefficient r. Critical Values of the Pearson Correlation Coefficient r he best predicted value of y is Round to two decimal places as needed.) Critical Values of the Pearson Correlation Coefficient r NOTE: To test H,: p=0 Jagainst H,: pz0, reject H, f the absolute value of r is greater than the critical value in the table. a =0.05 0.950 n a= 0.01 0.990 0.878 0.959 6 0.811 0.917 7 0.754 0.875 8 0.707 0.834 0.666 0.632 0.602 9 0.798 0.765 0.735 10 11 12 13 14 0.576 0.708 0.684 0.661 0.553 0.532 15 0.514 0.641 16 0.497 0623

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** The table below presents the critical values of the Pearson correlation coefficient (r) for different sample sizes (n) at two significance levels: α = 0.05 and α = 0.01. | n | α = 0.05 | α = 0.01 | |-----|----------|----------| | 9 | 0.666 | 0.798 | | 10 | 0.632 | 0.765 | | 11 | 0.602 | 0.735 | | 12 | 0.576 | 0.708 | | 13 | 0.553 | 0.684 | | 14 | 0.532 | 0.661 | | 15 | 0.514 | 0.641 | | 16 | 0.497 | 0.623 | | 17 | 0.482 | 0.606 | | 18 | 0.468 | 0.590 | | 19 | 0.456 | 0.575 | | 20 | 0.444 | 0.561 | | 25 | 0.396 | 0.505 | | 30 | 0.361 | 0.463 | | 35 | 0.335 | 0.430 | | 40 | 0.312 | 0.402 | | 45 | 0.294 | 0.378 | | 50 | 0.279 | 0.361 | | 60 | 0.254 | 0.330 | | 70 | 0.236 | 0.305 | | 80 | 0.220 | 0.286 | | 90 | 0.207 | 0.269 | | 100 | 0.196 | 0.256 | ### Explanation - **n**: Represents the sample size. - **α = 0.05**: The critical value of r at a 5
Transcribed Image Text:**Critical Values of the Pearson Correlation Coefficient r** The table below presents the critical values of the Pearson correlation coefficient (r) for different sample sizes (n) at two significance levels: α = 0.05 and α = 0.01. | n | α = 0.05 | α = 0.01 | |-----|----------|----------| | 9 | 0.666 | 0.798 | | 10 | 0.632 | 0.765 | | 11 | 0.602 | 0.735 | | 12 | 0.576 | 0.708 | | 13 | 0.553 | 0.684 | | 14 | 0.532 | 0.661 | | 15 | 0.514 | 0.641 | | 16 | 0.497 | 0.623 | | 17 | 0.482 | 0.606 | | 18 | 0.468 | 0.590 | | 19 | 0.456 | 0.575 | | 20 | 0.444 | 0.561 | | 25 | 0.396 | 0.505 | | 30 | 0.361 | 0.463 | | 35 | 0.335 | 0.430 | | 40 | 0.312 | 0.402 | | 45 | 0.294 | 0.378 | | 50 | 0.279 | 0.361 | | 60 | 0.254 | 0.330 | | 70 | 0.236 | 0.305 | | 80 | 0.220 | 0.286 | | 90 | 0.207 | 0.269 | | 100 | 0.196 | 0.256 | ### Explanation - **n**: Represents the sample size. - **α = 0.05**: The critical value of r at a 5
Suppose IQ scores were obtained for 20 randomly selected sets of siblings. The 20 pairs of measurements yield \( \bar{x} = 99.49 \), \( \bar{y} = 100.1 \), \( r = 0.884 \), P-value = 0.000, and \( y = 6.29 + 0.94x \), where \( x \) represents the IQ score of the younger child. Find the best predicted value of \( \hat{y} \) given that the younger child has an IQ of 104? Use a significance level of 0.05. **The best predicted value of \( \hat{y} \) is** [Input Box] (Round to two decimal places as needed.) --- **Critical Values of the Pearson Correlation Coefficient r** | n | \( \alpha = 0.05 \) | \( \alpha = 0.01 \) | |----|---------------------|---------------------| | 4 | 0.950 | 0.990 | | 5 | 0.878 | 0.959 | | 6 | 0.811 | 0.917 | | 7 | 0.754 | 0.875 | | 8 | 0.707 | 0.834 | | 9 | 0.666 | 0.798 | | 10 | 0.632 | 0.765 | | 11 | 0.602 | 0.735 | | 12 | 0.576 | 0.708 | | 13 | 0.553 | 0.684 | | 14 | 0.532 | 0.661 | | 15 | 0.514 | 0.641 | | 16 | 0.497 | 0.623 | | 17 | 0.482 | 0.606 | | 18 | 0.468 | 0.590 | | 19 | 0.456 | 0.575 | | 20 | 0.444 | 0.561 | | 25 | 0.396 | 0.505
Transcribed Image Text:Suppose IQ scores were obtained for 20 randomly selected sets of siblings. The 20 pairs of measurements yield \( \bar{x} = 99.49 \), \( \bar{y} = 100.1 \), \( r = 0.884 \), P-value = 0.000, and \( y = 6.29 + 0.94x \), where \( x \) represents the IQ score of the younger child. Find the best predicted value of \( \hat{y} \) given that the younger child has an IQ of 104? Use a significance level of 0.05. **The best predicted value of \( \hat{y} \) is** [Input Box] (Round to two decimal places as needed.) --- **Critical Values of the Pearson Correlation Coefficient r** | n | \( \alpha = 0.05 \) | \( \alpha = 0.01 \) | |----|---------------------|---------------------| | 4 | 0.950 | 0.990 | | 5 | 0.878 | 0.959 | | 6 | 0.811 | 0.917 | | 7 | 0.754 | 0.875 | | 8 | 0.707 | 0.834 | | 9 | 0.666 | 0.798 | | 10 | 0.632 | 0.765 | | 11 | 0.602 | 0.735 | | 12 | 0.576 | 0.708 | | 13 | 0.553 | 0.684 | | 14 | 0.532 | 0.661 | | 15 | 0.514 | 0.641 | | 16 | 0.497 | 0.623 | | 17 | 0.482 | 0.606 | | 18 | 0.468 | 0.590 | | 19 | 0.456 | 0.575 | | 20 | 0.444 | 0.561 | | 25 | 0.396 | 0.505
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