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:
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.
Just looking for some guidance or an example. Thanks
How would you interpret the correlation coefficient in terms of strength and direction?
In terms of strength, the correlation coefficient of -0.25 suggests a weak negative relationship between income and happiness. This means that as income increases, happiness tends to decrease, but the relationship is not very strong.
In terms of direction, the negative sign indicates that the relationship between income and happiness is negative. This means that as income increases, happiness levels tend to decrease, although again, the relationship is not very strong.
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?
Increasing the number of subjects in the study to one thousand would likely improve the reliability and accuracy of the overall correlation estimate. As the sample size increases, the results become more representative of the population, resulting in less sampling error and greater statistical power.
With more subjects, the variation in the data tends to decrease, leading to a more precise estimate of the correlation coefficient. This means that the correlation coefficient might not change significantly, but the increased sample size helps to provide more confidence and precision in the estimate of the 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.
Randomly selecting subjects is crucial for obtaining a sample that is truly representative of the population. It helps to minimize selection bias and increases the generalizability of the findings.
For example, let's say we are investigating the relationship between income and happiness in a city with a mixture of rich and poor neighborhoods. If we only select subjects from the wealthy neighborhoods, our sample may not represent the diversity of incomes and lifestyles within the city. This could lead to a biased estimate of the correlation between wealth and happiness.
By randomly selecting subjects from different neighborhoods, we ensure that each individual has an equal probability of being included in the study. This helps to avoid systematic bias and provides a representative sample that allows for valid inferences about the population as a whole.
In summary, random selection helps to ensure that a sample represents the population accurately, minimizing bias and increasing the generalizability of the findings.