Answer to Question #128214 in Statistics and Probability for Richard Olarte

Question

In a correlational study using the Pearson r formula, answer the hypothesis of:
There is no significant correlation between the height and weight by 10 students.
Data:
Students Height in Inches Weight in lbs.
A 62 108
B 62 144
C 61 115
D 60 110
E 59 100
F 56 115
G 62 88
H 62 100
I 66 94
J 62 125
Formula:

Answer 1

Pearson’s r Correlation

H0: There is no si gnificant correlation between the height and weight by 10 students.

H1: There is a significant correlation between the height and weight by 10 students.

We use the following Pearson’s r correlation formula

r = $\frac{\sum(x- x̄)(y-ȳ)}{\sqrt{\sum(x- x̄)^2(y-ȳ)^2}}$

Substituting the values on the formula, we get the following

$\frac{-69.8}{\sqrt{59.6*2374.9}} = -0.185528071$

The data provide evidence against the null hypothesis. The researchers therefore reject the null hypothesis and conclude that there is a statistically significant negative correlation between the height and weight by 10 students in the study.