A researcher wonders if there is a correlation between ( X ) people’s opinions o

Question

A researcher wonders if there is a correlation between (X) people’s opinions of bilingual education and (Y) their opinions about whether foreign-born citizens should be allowed to run for president. She collects the following data, with both variables being measured on a scale from 1 to 9 (1 being strongly opposed and 9 being strongly in favor).

X         Y

2         5

5         2

8         6

6         9

1         3

2         1

8         5

3         1

Calculate a Pearson’s correlation coefficient and determine whether the correlation is significant.

Explanation / Answer

The pearson correlation coefficient is computed as:

X Values
= 35 ( that is the sum of all X values )
Mx = Mean = 4.375 ( that is sum divided by the sample size which is 8 here )
(X - Mx)2 = SSx = 53.875

Similarly for Y values now:
Y Values
= 32
MY = Mean = 4
(Y - My)2 = SSy = 54

X and Y Combined
N = 8
(X - Mx)(Y - My) = 30

R Calculation
r = ((X - My)(Y - Mx)) / ((SSx)(SSy))
r = 30 / ((53.875)(54)) = 0.5562
r = 0.5562

Therefore the correlation coefficent between the 2 variables is 0.5562. This is a moderate positive relation between the 2 variables.

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