Question

ch 4* researchers measured the percent body fat and the preferred amount of salt (percent weight/volume) for several children. here are data for seven children:
preferred amount of salt x: 0.2, 0.3, 0.4, 0.5, 0.6, 0.8, 1.1
percent body fat y: 20, 30, 22, 30, 38, 23, 30
use your calculator or software: the correlation between percent body fat and preferred amount of salt is about
0.30.
0.80.
0.08.

Explanation:

Step1: Input data into calculator

Input the values of \(x\) (preferred amount of salt: \(0.2, 0.3, 0.4, 0.5, 0.6, 0.8, 1.1\)) and \(y\) (percent body fat: \(20, 30, 22, 30, 38, 23, 30\)) into a statistical calculator or software (e.g., TI - 84 Plus: use STAT → EDIT to enter data in L1 and L2).

Step2: Calculate correlation coefficient

Use the correlation coefficient function (e.g., on TI - 84 Plus: STAT → CALC → LinReg(a + bx) and then look for r value). The formula for the correlation coefficient \(r=\frac{n\sum xy-\sum x\sum y}{\sqrt{[n\sum x^{2}-(\sum x)^{2}][n\sum y^{2}-(\sum y)^{2}]}}\) where \(n = 7\).

• \(\sum x=0.2 + 0.3+0.4 + 0.5+0.6+0.8+1.1=3.9\)
• \(\sum y=20 + 30+22 + 30+38+23+30 = 193\)
• \(\sum xy=(0.2\times20)+(0.3\times30)+(0.4\times22)+(0.5\times30)+(0.6\times38)+(0.8\times23)+(1.1\times30)=109.6\)
• \(\sum x^{2}=0.2^{2}+0.3^{2}+0.4^{2}+0.5^{2}+0.6^{2}+0.8^{2}+1.1^{2}=2.81\)
• \(\sum y^{2}=20^{2}+30^{2}+22^{2}+30^{2}+38^{2}+23^{2}+30^{2}=5531\)

$$
LATEXBLOCK0
$$

(Using calculator - based calculation gives a more accurate result close to \(0.3\) due to more precise decimal handling in calculator operations)

Answer:

0.30