Problem 3 [13 marks]. In this problem, you will be examining data to estimate pr

Question

Problem 3 [13 marks]. In this problem, you will be examining data to estimate proba bility tables for the joint random variables of marijuana use and dance/party participation Dataset obtained from (http://www.stat.ufl.edu/ winner/datasets.html). You can read more about the format of the data and variable descriptions here. The study was conducted to determine if behaviour correlates with marijuana use among middle class youths and was published in 1976 (a bit outdated but interesting nonetheless!). The data is summarized below: Party/Dance Participation Not At All Somewhat A Great Deaow Totals 118 40 54 32 Never 40 1/month 17 Totals a) (2 marks) Using the count data in this problem, how many middle class youths were surveyed? Briefly explain how you might use the data presented to estimate each joint probability? For example, how could you use these counts to estimate the propor- tion of middle class youths or the probability that a middle class youth somewhat uses marijuana less than once a month and participates in dance/parties a great deal? b) (2 marks) Create an estimated joint probability table using the data provided. Verify c) (3 marks) Find the marginal probability mass table for marijuana use, and briefly d) (3 marks) What is the probability that a middle class youth that consumes marijuana e) (3 marks) Find the conditional probability mass table for dance/party participation that your probability sum to describe what information this table con veys daily will never participate at dance/parties? for middle class youths who rarely (

Explanation / Answer

Question 3 (a)

The total row/ Colum table is

HEre total middle class youth surveyed = 617

To calculate the joint probability for each type of cell like Never and not at all can be calculated by dividing the number of such persons divided by number of total persons.

(b) Joint probability table

(c) Marginal probability mass table for marijuana use

Here we can see that

For Pr(Marijuana use)= 0.6013 ; for marijuna use = never

= 0.1588 ; for marjuana use < 1/month

= 0.1605 ; for marijuana use > 1/month

= 0.0794 ; for marijuana use > 1/day

(This table conveys that in the sampe the probability of people who never use marijuana or used it <1/month, > 1/month or >1/day.

(d) Here we have to find that

Pr(Consumes marijuana daily will never particpte at dance/parties) = Pr(Never participate l marijuna daily) = 0/49 = 0

(e) Conditional probability mass table for dance/party participaton for middle class youths who rarely (< 1/month) consume marijuana.

Pr(dance prty participation l consume marijuana = < 1/month)

= 3/98 ; for no party at all

= 55/98 ; for Somewhat do prty

= 40/98 ; is party is a great deal

Party/Dance participation Not at all Somewh A gret deal total never 40 213 118 371 <1/month 3 55 40 98 >1/month 1 44 54 99 >1/day 0 17 32 49 Total 44 329 244 617

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