**Critical Values for Correlation Coefficient**This chart displays the critical values for correlation coefficients at different sample sizes, denoted by $ n $.| $ n $ | Critical Value ||-------|----------------|| 3 | 0.997 || 4 | 0.950 || 5 | 0.878 || 6 | 0.811 || 7 | 0.754 || 8 | 0.707 || 9 | 0.666 || 10 | 0.632 || 11 | 0.602 || 12 | 0.576 || 13 | 0.553 || 14 | 0.532 || 15 | 0.514 || 16 | 0.497 || 17 | 0.482 || 18 | 0.468 || 19 | 0.456 || 20 | 0.444 || 21 | 0.433 || 22 | 0.423 || 23 | 0.413 || 24 | 0.404 || 25 | 0.396 || 26 | 0.388 || 27 | 0.381 || 28 | 0.374 || 29 | 0.367 || 30 | 0.361 |These values are used to determine the significance of a correlation at various sample sizes. A high critical value indicates that a strong correlation is needed to achieve significance at smaller sample sizes, while a lower value suffices for larger samples. **Exploring Correlation Between Height and Head Circumference in Children**A pediatrician seeks to understand the potential relationship between a child's height and head circumference. A sample of 8 children is randomly selected, and their respective heights and head circumferences are measured. The findings are presented in the following table:| Height (in.) | Head Circumference (in.) ||--------------|--------------------------|| 27.5 | 17.2 || 25.5 | 17 || 26.25 | 17.1 || 25.25 | 17 || 27.5 | 17.6 || 26.25 | 17.4 || 25.75 | 17.1 || 26.75 | 17.4 |**Task (c):** Compute the linear correlation coefficient between height and head circumference.- **r = ____**- *(Round to three decimal places as needed.)*

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Description: **Critical Values for Correlation Coefficient**This chart displays the critical values for correlation coefficients at different sample sizes, denoted by $ n $.| $ n $ | Critical Value ||-------|----------------|| 3 | 0.997 || 4

Let, X : Height (in.), Y : Head circumference (in.).

Math

Statistics

A pediatrician wants to determine the relation that may exist between a child's height and head circumference. She randomly selects 8 children from her practice, measures their height and head circumference, and obtains the data shown in the table. Complete parts (a) through (e) below. O Click here to see the Table of Critical Values for Correlation Coefficient. Height (in.) Head Circumference (in.) - 27.5 25.5 26 25 25 25 17.2 17 27.5 26.25 25.75 26.75 17.1 17 17.6 17.4 17.1 17.4 (c) Compute the linear correlation coefficient between the height and head circumference of a child. (Round to three decimal places as needed.)

A pediatrician wants to determine the relation that may exist between a child's height and head circumference. She randomly selects 8 children from her practice, measures their height and head circumference, and obtains the data shown in the table. Complete parts (a) through (e) below. O Click here to see the Table of Critical Values for Correlation Coefficient. Height (in.) Head Circumference (in.) - 27.5 25.5 26 25 25 25 17.2 17 27.5 26.25 25.75 26.75 17.1 17 17.6 17.4 17.1 17.4 (c) Compute the linear correlation coefficient between the height and head circumference of a child. (Round to three decimal places as needed.)

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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Concept explainers

Inverse Normal Distribution

The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.

Mean, Median, Mode

It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.

Z-Scores

A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.

Topic Video

Question

**Critical Values for Correlation Coefficient**

This chart displays the critical values for correlation coefficients at different sample sizes, denoted by $ n $.

| $ n $ | Critical Value |
|-------|----------------|
| 3 | 0.997 |
| 4 | 0.950 |
| 5 | 0.878 |
| 6 | 0.811 |
| 7 | 0.754 |
| 8 | 0.707 |
| 9 | 0.666 |
| 10 | 0.632 |
| 11 | 0.602 |
| 12 | 0.576 |
| 13 | 0.553 |
| 14 | 0.532 |
| 15 | 0.514 |
| 16 | 0.497 |
| 17 | 0.482 |
| 18 | 0.468 |
| 19 | 0.456 |
| 20 | 0.444 |
| 21 | 0.433 |
| 22 | 0.423 |
| 23 | 0.413 |
| 24 | 0.404 |
| 25 | 0.396 |
| 26 | 0.388 |
| 27 | 0.381 |
| 28 | 0.374 |
| 29 | 0.367 |
| 30 | 0.361 |

These values are used to determine the significance of a correlation at various sample sizes. A high critical value indicates that a strong correlation is needed to achieve significance at smaller sample sizes, while a lower value suffices for larger samples.

**Exploring Correlation Between Height and Head Circumference in Children**

A pediatrician seeks to understand the potential relationship between a child's height and head circumference. A sample of 8 children is randomly selected, and their respective heights and head circumferences are measured. The findings are presented in the following table:

| Height (in.) | Head Circumference (in.) |
|--------------|--------------------------|
| 27.5 | 17.2 |
| 25.5 | 17 |
| 26.25 | 17.1 |
| 25.25 | 17 |
| 27.5 | 17.6 |
| 26.25 | 17.4 |
| 25.75 | 17.1 |
| 26.75 | 17.4 |

**Task (c):** Compute the linear correlation coefficient between height and head circumference.

- **r = ____**
- *(Round to three decimal places as needed.)*

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