Question

Each person in a random sample of 20 students at a particular university was asked whether he or she is registered to vote. The responses \((\mathrm{R}=\) registered, \(\mathrm{N}=\) not registered) are given here: \(\begin{array}{lllllllllll}\text { R R } & \text { N R } & \text { N } & \text { N R } & \text { R } & \text { R } & \text { N R R R R R N R R R } \mathrm{N}\end{array}\) Use these data to estimate \(\pi\), the true proportion of all students at the university who are registered to vote.

Short answer

The true proportion \(\pi\) of students at the university who are registered to vote is calculated by dividing the number of students who are registered to vote (\(R\)) by the total sample size (20). After counting \(R\) and computing \(\pi = \frac{R}{20}\), you obtain the estimated value of \(\pi\).

Step-by-step solution

Interpret the data

The data presents a series of 'R' and 'N' responses. 'R' signifies that the student in the sample is registered to vote, while 'N' means the student is not registered. From this, we see we're given: \[ R, R, N, R, N, N, R, R, R, R, N, R, R, R, N, R, R, R \]

Count the sample size and the registered students

The sample size is 20 (since 20 students were surveyed). Count the number of times 'R' appears in the data and denote it by \(R\). This tells us the number of students in the sample that are registered to vote.

Compute the proportion of registered students

To compute the proportion \(\pi\) of registered students, you must divide the number of registered students (\(R\)) by the total sample size. This calculation is represented by the formula: \(\pi = \frac{R}{20}\)

Perform the calculation

After counting the total number of registered students (\(R\)), insert this value into the formula from Step 3 and perform the computation. This will yield the estimated proportion \(\pi\) of registered students at the university.