3. MARITAL STATUS AND AGE A study was conducted at a Daytona Beach nightclub to

Question

3. MARITAL STATUS AND AGE

A study was conducted at a Daytona Beach nightclub to examine whether or not there was a link between age and marital status. A total of 140 customers at the nightclub were surveyed and asked about confidential questions regarding their age and what their marital status was. 49 of the customers were at least 30 years of age, the rest were under 30. 105 of the customers were single, the rest were married. 21 of customers were 30 or over in age and married.

Use marginal probabilities to comment on the age of customers attending the nightclub

Use marginal probabilities to comment on the marital status of customers attending the nightclub

What is the probability of randomly selecting a customer of the nightclub and finding that he or she is under the age of 30 and single?

If a randomly selected customer of the nightclub is under the age of 30, what is the probability that he or she is single?

Is marital status independent of age? Explain carefully.

Explanation / Answer

from given data:

dividing each cell with 140;

1) here as marginal probability fo <30 yrs is( 0.65) higher than >30 year (0.35) we can say that people who are less than 30 years are more inclined to attend the nightclub then with age >30 years

2) as marginal probability for single is( 0.75) higher than married (0.25) we can say that people who are single are more inclined to attend the nightclub then with married people

3)probability of randomly selecting a customer of the nightclub and finding that he orshe is under the age of 30 and single =0.55

4) P(single|<30) =0.55/0.65 =0.8462

5)as P(single|<30) is not equal to P(single ) which is 0.75. threfore marital status is not independent of age

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