Question

question 6 of 10
three national news networks are trying to estimate what percentage of american voters support a particular presidential candidate. to estimate the population parameter, each of the three networks collect data from a simple random sample of voters. here are the numbers of voters in the networks’ random samples:

• network a: 3800 voters sampled
• network b: 3500 voters sampled
• network c: 3250 voters sampled

which sample is likely to have the least variability?
a. the network a sample
b. the network b sample
c. the network c sample

Explanation:

Step1: Recall sampling variability rule

For simple random samples, larger sample sizes correspond to lower variability (smaller standard error, where standard error = $\frac{\sigma}{\sqrt{n}}$, with $\sigma$ as population standard deviation and $n$ as sample size).

Step2: Compare sample sizes

Network A: $n=3800$, Network B: $n=3500$, Network C: $n=3250$. $3800 > 3500 > 3250$.

Step3: Identify least variability

Largest sample (Network A) has least variability.

Answer:

A. The Network A sample