Monika Szkoda Problem 10.docx

Problem 10)

Using an appropriate test statistic calculate minimum (in absolute value) statistically significant value of correlation coefficient for sample size of 25 and significance level α=0.05

Solution:

Given data:

n= 25                            size of the sample
α= 0.05                            significance level
df= 23                            degrees of freedom

Test based on Student`s t-distribution

H0:              If H0 is true, than rxy is close (near) to zero (0) – Null Hypothesis
H1:              If H1 is true, than rxy is far away from zero (0) – Alternative Hypothesis

Critical value:
t0.05;23=2.06866                             (taken from the table for Student`s t –distribution for α= 0.05 and df= 23)

Test statistic:

t=rxy1-rxy2∙n-2

                                                        2.06866=rxy1-rxy2∙23  (both sides raise to the power of two)

                                                             4.27935=rxy21-rxy2∙23 (divide both sides on 23 and multiply by (1-rxy2))

0.186058-0.186058rxy2=rxy2

0.186058=1.18605rxy2

rxy2=0.156872
After calculation:

rxy=0.396071

Answer:
The minimum statistically significant value (in absolute value) of the correlation coefficient for given sample equals to 0.396071