SOLUTION: You are interested in knowing whether wealthier people are happier. You collected data from fifty people about their incomes and their overall happiness levels on a scale of 1 to 1

Question 1190269: You are interested in knowing whether wealthier people are happier. You collected data from fifty people about their incomes and their overall happiness levels on a scale of 1 to 10. Upon analyzing the results, you find that the correlation coefficient has a value of −0.25. On the basis of this data, respond to the following:
How would you interpret the correlation coefficient in terms of strength and direction?
How would the results be affected if you increased the number of subjects in the study to one thousand? Why might that affect the overall correlation?
How important is it to randomly select subjects? Explain in detail using an example of a sample that might not be truly representative of the population.
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
A correlation of -0.25 is weak. it would lean slightly towards wealthy people's being less happier, but again this issue is a correlation and not a strong one. You also don't know whether this is statistically significant, which with 50 people may not be. So there may be no difference at all.
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With 1000 people it is far more likely for a correlation to be statistically significant different from 0. That doesn't mean it is much of a correlation however.
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These have to be done randomly and since there are numerous variables that affect happiness, including where one lives, how the question is formulated, and what happiness really is (plus meaning different things to different people, as the song goes).
A non-representative sample of the population may be people in a city, which may not be representative of larger or smaller cities, let alone representative of those in rural areas. Cultural differences not controlled are another issue as well.

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