Question

445 college students were classified according to both frequency of marijuana use and parental use of alcohol and psychoactive drugs (from the article \marijuana use in college\, youth and society, 1979: 323 - 334). the data are represented in the contingency table shown below.

parental usage	student usage level
both		17	11	19	47
neither		141	54	40	235
one		68	44	51	163
total		226	109	110	445

which of the following is the marginal distribution for student usage level?

never = 17/445, occasional = 11/445, regular = 19/445
never = 110/445, occasional = 54/445, regular = 226/445
never = 226/445, occasional = 109/445, regular = 110/445
never = 141/226, occasional = 54/109, regular = 40/110

Explanation:

Step1: Recall marginal distribution concept

Marginal distribution of student usage level is found by dividing row - totals of student usage levels by the grand total.

Step2: Identify relevant totals

The total number of students who never used is 226, occasional users is 109 and regular users is 110. The grand total of students is 445.

Step3: Calculate probabilities

The probability of never using is $\frac{226}{445}$, occasional using is $\frac{109}{445}$ and regular using is $\frac{110}{445}$.

Answer:

Never = 226/445, Occasional = 109/445, Regular = 110/445