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 1187761: 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!
Low negative correlation.
If the sample size were 1000, the correlation has increased likelihood of being statistically significant. That's one possibility. Another is that a there are too few wealthy people in a sample of 50 to mean much of anything. A third issue is that wealth isn't clear here. A fourth issue might be that with 1000, there are more wealthy people so that the correlation may no longer be negative.
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Non-random sample: taken from center city, suburbs, the state, people chosen in the sample who will not reply, give a wrong value. For a sample to be random, every person in the population must have a non-zero probability of being chosen. The likelihood may be very close to zero, but it is not zero. If a whole swath of the country is not considered, for example, the sample is not random. Those are some of the reasons. Sampling technique (SRS, stratified, systematic, cluster) also needs to be appropriate.
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