# Correlation Coefficient

X Y

90 10

86 9

94 7

70 6

86 7

90 15

94 10

66 5

98 11

86 9

1. Calculate and interpret the mean and standard deviation for variables X and Y. (5 points)

2. Calculate and interpret the Pearson's correlation coefficient between test scores (X) and

number of hours a person studied for the test (Y). (10 points)

3. Determine if the coefficient is statistically significant and tell me how you reach that

conclusion. (10 points)

4. Based on your prior answer, reject/accept null hypothesis (2-tailed) and tell me what that

means. (5 points)

https://brainmass.com/statistics/pearson-product-moment-correlation/correlation-coefficient-240891

#### Solution Preview

1. Calculate and interpret the mean and standard deviation for variables X and Y. (5 points)

I did this in Excel (see the attached file). Here are the means and standard deviations for X and Y:

mean of X: 86

std. dev. of X: 10.328

mean of Y: 8.9

std. dev. of Y: 2.885

2. Calculate and interpret the Pearson's correlation coefficient between test scores (X) and

number of hours a person studied for the test (Y). (10 points)

I also did this in Excel, by using the Excel function =PEARSON(y-values, x-values). The correlation coefficient is:

r = ...