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. 1. Use marginal probabilities to comment on the age of customers attending the nightclub 2. Use marginal probabilities to comment on the marital status of customers attending the nightclutb 3. What is the probability of randomly selecting a customer of the nightclub and finding that he or she is unde of 30 and single? 4 f randomly selected customer ot the nightclub is under the age or 30, wrat is the proability that he or sthe is single? S. is marital status independent of age? Explain caretully DELL

Explanation / Answer

For Marginal or Conditional Probabilities, it is best advised to put the numbers in a tabular format.

a) Age of customers attending night club

Less than 30 = 91/140 = .65 ~ 65%

Greater than and equal to 30 = 49/140 = 0.35 ~ 35%.

b) Maritial Status of persons attending the night club.

Unmarried = 105/140 = 0.75 ~ 75%

Marrie = 35/140 = 0.25 ~ 25%

c) Randomly selecting a customer with age less than 30 and single.

Looking at the table, 77 is the number of persons less than 30 and unmarried.

Therefore, the prob. is 77/140 = 0.55

d) Selecting customer under the age of 30 and finding he or she is single.

Again, checking the table, total number of persons less than 30 = 91

No. of unmarried person in that age category = 77

P(A/B) = 77/91 = 0.85

e) Looking at the data above, we cannot say that marriage is independent of Age.

Since married data is spread across both the categories i.e. less than 30 and more than 30 as well.

Marital Status Married Unmarried Total Age <30 14 77 91 >=30 21 28 49 Total 35 105 140

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