You are interested in knowing whether wealthier people are happier. You collecte

Question

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.

Explanation / Answer

Here it is given that r=-0.25 which means this is weak negative correlation.

Now here n=50, if we increase the sample size to 1000 it is but obvious that we will get more data so the analysis become more accurate. In other sense in 50 people if 50% refuse to give answer we will end up with only data of 25, but in case of 1000 if 50% refuses we still have n=500 a big number.

It is very important to select data randomly because randomly selected data are biased free and gives unbiased estimator for population.

Let us consider an example of students interested for youth festival in a college. If I collect consider statistics class as a sample and get data of all the students this will not be a representative of the population here which is college.

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