Question

23. Statistics Canada cross-classified 400 18-24 year olds as to whether or not they attended university in 2001 and what income group their parents belong to. They wanted to see if university attendance depends on parents income. The results are shown below. Parent's Income Below $50,000 $50,000 - $100,000 Above $100,000 Total Attended Yes 20 73 27 120 University? No 80 167 33 280 400 Total 100 240 60 (a) What percentage of 18-24 year olds has parents whose income is at least $50,000? Answer: (b) If an 18-to 24 year old has parents whose income is at least $50,000, what is the probability that they attended university in 2001?

Answer 1

We would be looking at the first 4 parts here as:

a) The percentage of 18-24 year olds that have income of at least $50,000 is computed here as:
= P(At least 50,000)

= n(At least 50,000) / n(Total)

= (240 + 60)/400 = 0.75

Therefore 0.75 or 75% is the required percentage here.

b) Given that the income is at least $50,000, the probability that they attended university is computed using Bayes theorem here as:
P(Attended university | at least 50,000)

= n(Attended university and at least 50,000) / n(At least 50,000)

= (73 + 27) / 300

= 1/3

Therefore 1/3 = 0.3333 is the required probability here.

c) Given that a university was not attended, the probability that the income was at most 100,000 is computed using Bayes theorem here as:

P(X <= 100,000 | did not attend)

= n(X <= 100,000 and did not attend) / n(did not attend)

= (80 + 167) / 280 = 0.8821

Therefore 0.8821 is the required probability here.

d) Given that the income is at most 100,000 probability that the person attended the university is computed here as:
= P(Attended university | <= 100,000)

= n(Attended university and <= 100,000 )/ n( <= 100,000)

= (20 + 73) / (240 + 100)

= 93 / 340

= 0.2735

Therefore 0.2735 is the required probability here.