Question

Attitudes toward alcohol At a party, there are $30$ students over age $21$ and $20$ students under age $21$ You choose at random 3 of those over 21 and separately choose at random $2$ of those under $21$ to interview about attitudes toward alcohol. You have given every student at the party the same chance to be interviewed: what is the chance? Why is your sample not an SRS?

Short answer

A sample of $5$ students beyond the age of $21$ or a sample of $5$ students under the age of $21$ have no possibility of being interviewed.

Step-by-step solution

Given information

There are $30$ students over the age of $21$ and $20$ students under the age of $21$ at a party. You pick three people over the age of $21$ and two people under the age of $21$ at random to interview about alcohol.

Concept

A sample survey picks a group of people from a larger group of people about whom we want to learn more. The data from the sample is used to draw inferences about the population. It's critical to be specific about the demographic you're interested in and the characteristics you'll track.

Explanation

There are $30$ students over the age of $21$ and $20$ students under the age of $21$ at a party. Every student has an equal opportunity to be interviewed.

To choose three pupils over the age of $21$from a group of thirty. Every student above the age of $21$has a $3/30=1/10$probability of being interviewed.

To choose two pupils under the age of $21$from a group of twenty. Every student under the age of $21$has a $2/20=1/10$probability of being interviewed. In both cases, this is $1/10$ An SRS ensures that any sample of a given size has the same chance of being chosen. It is not an SRS because not all students in each sample have the same chance of being questioned. In this case, a sample of $5$ students beyond the age of $21$ or a sample of $5$ students under the age of $21$ have no possibility of being interviewed.