Question
In: Statistics and Probability
If a researcher found that there was a correlation of r = -0.67 between the number...
If a researcher found that there was a correlation of r = -0.67 between the number of siblings a person has and introversion, and the researcher sampled n = 30 people, what conclusions can you make about this relationship
Solutions
Expert Solution
The correlation coefficient is -0.67. Hence it is clear that there is a negative linear relationship between the number of siblings a person has and introversion. The strength of the linear relationship is fairly strong.
Significance test
We will check whether the correlation coefficient is significant or not, say at a 5% level of significance.
The following needs to be tested:
where 
corresponds to the population correlation.
The sample size is n=30, so then the number of degrees of freedom is df=n−2=30−2=28
The corresponding critical correlation value rc for a significance level of α=0.05, for a two-tailed test, is:
Observe that in this case, the null hypothesis H0:ρ=0 is rejected if |∣r∣>rc=0.361.
Based on the sample correlation provided, we have that ∣r∣=0.67>rc=0.361, from which it is concluded that the null hypothesis is rejected and therefore there seems to be a significant correlation between the two variables.
Let me know in the comments if anything is not clear. I will reply ASAP! Please do upvote if satisfied!
orchestra answered 1 year agoRelated Solutions
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