Question

ou 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 1

1.The correlation coefficient here shows that there is a negative linear relationship between the variables.Here negative relationship means that if one of the variables tend to increase then the other variable tend to decrease.while the small values of the coefficient that variables are not much linearly related.

2.If the number of subjects is incresed it will result in a better idea about the population.Hence if there is a number of of subjects the result will tend to give us the true relationship of the variables.

3.It is very to select random subjects,because this will result in giving us the correct idea of the population.We can show it by a example:supoose we want to know the per capita income of a state and if we select our subjects only from the urban porshe population then this will mislead us about the per capita income of the state.