Question

1. A simple random sample of adults living in a suburb of Philadelphia was selected. The age (random variable X) and annual income (random variable Y) of each adult in the sample were recorded with the results summarized in the table below. Annual Income Age Category $25,000 $35,000 $35,001-$50,000 Over $50,000 Total 21-30 8 15 27 50 31 45 22 32 35 89 46-60 12 14 27 53 Over 60 7 15 Total 47 64 96 207 3 a) Find the covariance and correlation coefficient of X and Y. Discuss the results. b) Based on the above data, would you argue that in this population annual income is independent of age?

Answer 1

Answer: Given that covariance and @ The correlation Co-efficient of ix and y. p(31-45 ) = +0- 4300 300 207 And P (over $50,000 and 3145 age category ) :35 207 =10.1691

© 207, Besed on above data, Population annual income is independent of age P(31-45) age = 10:4300 p (over $50,000) 9 = 6.4638) Hence sp (31-45. age category ) xp (ovai $ 50,000) 30.43 0.468 = [0.1994) So, we can say that 0.1994 +0.1691 So, we can not say that population annual income is independent of age. Note: If you satisfy with my solution, please give me a thumb up.