A club has 30 student members and 10 faculty members. The...

$A$ club has 30 student members and 10 faculty members. The students are $$ \begin{array}{lllll} \hline \text { Abel } & \text { Fisher } & \text { Huber } & \text { Miranda } & \text { Reinmann } \\ \text { Carson } & \text { Ghosh } & \text { Jimenez } & \text { Moskowitz } & \text { Santos } \\ \text { Chen } & \text { Griswold } & \text { Jones } & \text { Neyman } & \text { Shaw } \\ \text { David } & \text { Hein } & \text { Kim } & \text { 0'Brien } & \text { Thompson } \\ \text { Deming } & \text { Hernandez } & \text { Klotz } & \text { Pearl } & \text { Utts } \\ \text { Elashoff } & \text { Holland } & \text { Liu } & \text { Potter } & \text { Varga } \\ \hline \end{array} $$ $$ \text { The faculty members are } $$ $$ \begin{array}{lllll} \hline \text { Andrews } & \text { Fernandez } & \text { Kim } & \text { Moore } & \text { West } \\ \text { Besicovitch } & \text { Gupta } & \text { Lightman } & \text { Phillips } & \text { Yang } \\ \hline \end{array} $$ The club can send 4 students and 2 faculty members to a convention. It decides to choose those who will go by random selection. Describe a method for using Table $\mathrm{D}$ to select a stratified random sample of 4 students and 2 faculty. Then use line 123 to select the sample.

$A$ club has 30 student members and 10 faculty members. The students are $$
\begin{array}{lllll}
\hline \text { Abel } & \text { Fisher } & \text { Huber } & \text { Miranda } & \text { Reinmann } \\
\text { Carson } & \text { Ghosh } & \text { Jimenez } & \text { Moskowitz } & \text { Santos } \\
\text { Chen } & \text { Griswold } & \text { Jones } & \text { Neyman } & \text { Shaw } \\
\text { David } & \text { Hein } & \text { Kim } & \text { 0'Brien } & \text { Thompson } \\
\text { Deming } & \text { Hernandez } & \text { Klotz } & \text { Pearl } & \text { Utts } \\
\text { Elashoff } & \text { Holland } & \text { Liu } & \text { Potter } & \text { Varga } \\
\hline
\end{array}
$$ $$
\text { The faculty members are }
$$ $$
\begin{array}{lllll}
\hline \text { Andrews } & \text { Fernandez } & \text { Kim } & \text { Moore } & \text { West } \\
\text { Besicovitch } & \text { Gupta } & \text { Lightman } & \text { Phillips } & \text { Yang } \\
\hline
\end{array}
$$ The club can send 4 students and 2 faculty members to a convention. It decides to choose those who will go by random selection. Describe a method for using Table $\mathrm{D}$ to select a stratified random sample of 4 students and 2 faculty. Then use line 123 to select the sample.

Key Concepts

Stratified Random Sampling

Stratified random sampling involves dividing the overall population into subgroups, or strata, based on a shared characteristic (for example, students and faculty), and then randomly selecting samples from each subgroup. This method ensures that each subgroup is adequately represented in the sample, which increases the accuracy of any inferences made about the entire population.

Random Number Tables

A random number table is a tool that contains a sequence of digits generated in such a way that every number has an equal probability of occurrence. In sampling, these tables are used by assigning each individual a unique numeric label and then selecting numbers from the table. This method helps ensure that the selection process is unbiased and truly random. In the context of the question, one would use a specific line (line 123) from the table to generate the numbers needed for selecting the designated number of members from each stratum.

Transcript

00:01 So you have a situation in which you have a list of 30 students and you have 10 faculty, and you want to choose four students at random to go to a convention and two faculty members to go to a convention.

00:10 We're to use this line in your table.

00:13 So i would assign a two -digit number to each of the students, and the students would be 0 through 29 to these students.

00:28 And just have the first student, abel would be 0 ,0, then.

00:32 01 would be carson and so on all the way until you get to the last person.

00:37 And then i would assign a two -digit number to, i'm sorry, a one -digit number to each of the faculty members.

00:50 Because we have 10 faculty members, we can use a one -digit number to each faculty.

00:59 And so they will be numbered from the first person, andrews would get the number zero all the way up to the last.

01:05 Person would get the digit 9 and then i'm going to start at row 123 and we will discard discard for here all numbers that are from 30 to 99 now i can reassign each number so that i end up having all the digits being used but we want to describe a method for this and then we want to use the line to select our sample so let's start getting the numbers i'll write down the first digits of line 123.

01:39 I'll have to go kind of back and forth.

01:45 54580, 54580.

01:46 And let me just keep writing these down.

01:49 The next group is 81507, 81507.

01:54 81507...

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