Question

a survey by the pew research center (“Snapshots goals of gen next

APPLYING THE CONCEPTS 4.46 A survey by the Pew Research Center ("Snapshots: Goals of 'Gen Next' vs. 'Gen X," USA Today, March 27, 2007, p. 1A) indicated that 81% of 18-to 25-year-olds had getting rich as a goal, as compared to 62% of26-to 40-year- olds. Suppose that the survey was based on 500 respondents from each of the two groups. a. Form a contingency table. b. Give an example of a simple event and a joint event. c. What is the probability that a randomly selected respon- dent has a goal of getting rich? d. What is the probability that a randomly selected respon- dent has a goal of getting rich and is in the 26- to 40- year-old group? e. Are the events "age group" and "has getting rich as a goal" independent? Explain.

Answer 1

4.46

(a) Here total 18-25 years old = 500

total 26-40 year old = 500

Total who wants to be rich in 18-25 year old = 500 * 0.81 = 405

total who dont want to be rich in 18-25 year old = 500 - 405 = 95

Total who wants to be rich in 26-40 year old = 500 * 0.62 = 310

total who dont want to be rich in 26-40 year old = 500 - 310 = 190

Contigency table is given below

	Rich goal	Not Rich Goal	Total
18- 25 years old	405	95	500
26-40 years old	310	190	500
Total	715	285	1000

(b) Simple events are the events where one experiment happens at a time and it will be having a single outcome.

so here tossing a coin is a simple event. Or in the given problem, probability of selecting a 18-25 year old is a single event.

Joint event is a statistical measure that calculates the likelihood of two events occurring together and at the same point in time.  Like getting a 6 in dice and heads in a coin simultaneously is a joint event. In this case, getting a 18-25 year old having goal of being rich is a joint event.

(c) Probability of a random respondent of getting rich = Total aspired to be rich/Total population = 715/1000 = 0.715

(d) Pr(Getting rich and is in the 26 to 40 year old group) = 310/1000 = 0.310

(e) Here two events A and B would be independent if

P(A and B) = P(A) P(B)

so here

Pr(18 - 25 age group) = 0.5

Pr(getting rich) = 0.715

Pr(18 - 25 age group and getting rich) = 405/1000 = 0.405

so here,

Pr(18 - 25 age group) * Pr(Getting rich) = 0.5 * 0.715 = 0.3575 which is not equals to 0.405

so the events are not independent in nature.