uppose IQ scores were obtained for 20 randomly selected sets of siblings. The 20 pairs of measurements yield x= 97.71, y = 96.65, r= 0.874, P-value = 0.000, and y = 1.21 +0.98x, here x represents the IQ score of the older child. Find the best predicted value of y given that the older child has an IQ of 110? Use a significance level of 0.05. 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 isO Round to two decimal places as needed.) Critical Values of the Pearson Correlation Coefficient r INOTE: To test Ho p= 0 jagainst H,: p#0, reject if the absolute value of r greater than the critical value in the table. - 0.01 0.990 = 0.05 0.950 0.878 0.811 0.754 0.707 0.959 0.917 0.875 0.834 0.798 0.765 0.735 0.708 0.684 0.661 0.641 0.623 0.606 0.590 0.575 0.561 0.505 0.463 0.430 0.402 0.378 0.361 0.330 0.305 0.286 0.269 0.256 0.666 0.632 10 11 12 13 14 0.602 0.576 0.553 0.532 0.514 0.497 0.482 0.468 0.456 0.444 0.396 0.361 0.335 0.312 0.294 0.279 0.254 0.236 0.220 15 16 17 18 19 20 25 30 35 40 45 50 60 70 80 90 100 0.207 0.196
uppose IQ scores were obtained for 20 randomly selected sets of siblings. The 20 pairs of measurements yield x= 97.71, y = 96.65, r= 0.874, P-value = 0.000, and y = 1.21 +0.98x, here x represents the IQ score of the older child. Find the best predicted value of y given that the older child has an IQ of 110? Use a significance level of 0.05. 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 isO Round to two decimal places as needed.) Critical Values of the Pearson Correlation Coefficient r INOTE: To test Ho p= 0 jagainst H,: p#0, reject if the absolute value of r greater than the critical value in the table. - 0.01 0.990 = 0.05 0.950 0.878 0.811 0.754 0.707 0.959 0.917 0.875 0.834 0.798 0.765 0.735 0.708 0.684 0.661 0.641 0.623 0.606 0.590 0.575 0.561 0.505 0.463 0.430 0.402 0.378 0.361 0.330 0.305 0.286 0.269 0.256 0.666 0.632 10 11 12 13 14 0.602 0.576 0.553 0.532 0.514 0.497 0.482 0.468 0.456 0.444 0.396 0.361 0.335 0.312 0.294 0.279 0.254 0.236 0.220 15 16 17 18 19 20 25 30 35 40 45 50 60 70 80 90 100 0.207 0.196
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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![**Analysis of Sibling IQ Scores**
Suppose IQ scores were obtained for 20 randomly selected sets of siblings. Here's the data summary:
- 20 pairs of measurements
- Mean IQ of older child (\( \bar{x} \)): 97.71
- Mean IQ of younger child (\( \bar{y} \)): 96.65
- Correlation coefficient (r): 0.874
- P-value: 0.000, indicating statistical significance
- Regression equation: \( \hat{y} = 1.21 + 0.98x \)
**Task:**
Find the best predicted value of \( \hat{y} \) given that the older child has an IQ of 110 using a significance level of 0.05.
**Graph: Critical Values of the Pearson Correlation Coefficient (r)**
This table provides the critical values for the correlation coefficient at different significance levels (\( \alpha = 0.05 \) and \( \alpha = 0.01 \)), based on sample size (n).
- **Sample Size (n):** Ranges from 4 to 100
- **Critical values for \( \alpha = 0.05 \):** Start at 0.950 for n=4 and decrease to 0.196 for n=100.
- **Critical values for \( \alpha = 0.01 \):** Start at 0.990 for n=4 and decrease to 0.256 for n=100.
**Usage Note:**
To test \( H_0: \rho = 0 \) against \( H_1: \rho \neq 0 \), reject \( H_0 \) if the absolute value of r is greater than the critical value in the table.
**Calculation:**
Using the provided regression equation, calculate \( \hat{y} \) for an older child IQ of 110:
\[ \hat{y} = 1.21 + 0.98 \times 110 \]
The best predicted value of \( \hat{y} \) is (Round to two decimal places as needed).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fd738ea4e-7dd9-4a93-94a4-9a76a5585029%2F50cb614f-12bd-4582-a0f2-f4dd9d5d1ce4%2Flo88vmn_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Analysis of Sibling IQ Scores**
Suppose IQ scores were obtained for 20 randomly selected sets of siblings. Here's the data summary:
- 20 pairs of measurements
- Mean IQ of older child (\( \bar{x} \)): 97.71
- Mean IQ of younger child (\( \bar{y} \)): 96.65
- Correlation coefficient (r): 0.874
- P-value: 0.000, indicating statistical significance
- Regression equation: \( \hat{y} = 1.21 + 0.98x \)
**Task:**
Find the best predicted value of \( \hat{y} \) given that the older child has an IQ of 110 using a significance level of 0.05.
**Graph: Critical Values of the Pearson Correlation Coefficient (r)**
This table provides the critical values for the correlation coefficient at different significance levels (\( \alpha = 0.05 \) and \( \alpha = 0.01 \)), based on sample size (n).
- **Sample Size (n):** Ranges from 4 to 100
- **Critical values for \( \alpha = 0.05 \):** Start at 0.950 for n=4 and decrease to 0.196 for n=100.
- **Critical values for \( \alpha = 0.01 \):** Start at 0.990 for n=4 and decrease to 0.256 for n=100.
**Usage Note:**
To test \( H_0: \rho = 0 \) against \( H_1: \rho \neq 0 \), reject \( H_0 \) if the absolute value of r is greater than the critical value in the table.
**Calculation:**
Using the provided regression equation, calculate \( \hat{y} \) for an older child IQ of 110:
\[ \hat{y} = 1.21 + 0.98 \times 110 \]
The best predicted value of \( \hat{y} \) is (Round to two decimal places as needed).
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