Correlation Assignment: Statistical Analysis of IQ, Weight, and Income

This assignment presents two correlation problems designed to assess the student's understanding of statistical analysis. The first problem focuses on determining the correlation between IQ scores of identical twins. The student calculates the Pearson correlation coefficient (r), tests the significance of the relationship using a critical value and alpha level of .05, and interprets the coefficient of determination. The second problem investigates the correlation between weight category and income for a group of women professionals. The student calculates the Pearson correlation coefficient, tests its significance using a critical value and alpha level of .01, and interprets the coefficient of determination. For both problems, the student states the null and alternative hypotheses, shows all work, and includes a scatterplot to visually represent the data and the calculated correlation. The assignment demonstrates the application of correlation analysis in real-world scenarios, emphasizing hypothesis testing and interpretation.

Correlation Assignment
You are presented with 2 correlation problems to calculate below. Be sure to fill in
everything. Use your correlation and regression guide and example problem to help you
with your assignment. Remember to show your work!
Problem #1:
Correlation
A study was done to establish whether or not a relationship exists between IQ scores of
identical twins.
What is the null hypothesis?
There is no relationship between IQ score among the identical twins.
What is the alternative hypothesis?
There is a relationship between IQ score among the identical twins.
X
Twin A
X2 Y
Twin B
Y2 (X)(Y)
106 11236 115 13225 12190
127 16129 117 13689 14859
85 7225 89 7921 7565
73 5329 61 3721 4453
102 10404 98 9604 9996
85 7225 100 10000 8500
97 9409 98 9604 9506
110 12100 108 11664 11880
∑X =785
(∑X)2 =616225
∑X2 =79057 ∑Y =786
(∑Y)2 =617796
∑Y2 =79428 ∑XY =78949
n (number of paired values) = 8
Syllabus Page 1 of 5

r = ______(n) (∑XY) – (∑X) (∑Y)________
[ (n) (∑X2) – (∑X)2] [ (n) (∑Y2) – (∑Y)2 ]
r = ______(8) (78949) – (785) (786)________
[(8) (79057) – (616225)] [ (8) (79428) – (617796) ]
r = ______631592 – 617010________
[16231] [17628 ]
= 14582/ 16915.08
= 0.86
df =8-2
= 6
Use Alpha level .05, the significance value from the Critical Value for the Pearson Correlation is = 0.707
Is the relationship significant? Explain.
Yes the relationship is significant. Because the Pearson r-outcome is greater than the critical value.
R or r2 (coefficient of determination) = 73%
Insert a picture of your scatterplot below. To plot your values, go to the following site/applet:
http://www.shodor.org/interactivate/activities/ScatterPlot/ Your “assignment guide” provides step-by-step
instructions for using this applet.
Syllabus Page 2 of 5

Scroll down for Problem #2
Problem #2:
Syllabus Page 3 of 5

A study was done to compare weight and income for a group of women professionals. The
women were classified into one of five categories for weight: 1 = thinnest to 5 = heaviest.
Income figures are annual income (in thousands), rounded to the nearest $1,000.
What is the null hypothesis?
There is no relationship between the weight and income.
What is the alternative hypothesis?
There is a relationship between the weight and income
Pearson-r coefficient
X
Weight category
X2 Y
Income
Y2 (X)(Y)
1 1 125 15625 125
2 4 78 6084 156
4 16 49 2401 196
3 9 63 3969 189
5 25 35 1225 175
2 4 84 7056 168
5 25 38 1444 190
3 9 51 2601 153
1 1 93 8649 93
4 16 44 1936 176
∑X =
30
(∑X)2 =
900
∑X2 =110 ∑Y =
660
(∑Y)2 =435600
∑Y2 =50990 ∑XY =1621
n (number of paired values) =10
r = ______(n) (∑XY) – (∑X) (∑Y)________
[ (n) (∑X2) – (∑X)2] [ (n) (∑Y2) – (∑Y)2 ]
r = = ______(10) (1621) – (30) (660)________
Syllabus Page 4 of 5

[ (10) (110) – (900)] [ (10) (50990) – (435600)]
= -3590/ 3854.86
= -0.93
df =10-2
= 8
Use Alpha level .01, significance value from the Critical Value for the Pearson Correlation is = 0.765
Is the relationship significant? Explain.
In this case there are two situations. When the Pearson r-outcome is greater than the critical value then the
relationship is significant and when the Pearson r-outcome is less than the critical value then the relationship is not
significant. Because in this example r outcome is negative and the critical value is both positive and negative.
R or r2 (coefficient of determination) = 86.5%
Present a picture of your scatterplot. To plot your values, go to the following site/applet:
http://www.shodor.org/interactivate/activities/ScatterPlot/
Syllabus Page 5 of 5