Question

jason and yolanda both drew a simple random sample from a non - normally distributed population of 25,000. jasons sample consisted of 0.24% of the population, while yolandas sample consisted of 0.27% of the population. whose sample can be used to make references about the population?

• neither jasons sample nor yolandas sample
• only jasons sample
• only yolandas sample
• both jasons sample and yolandas sample

Explanation:

To determine whose sample can be used, we use the Central Limit Theorem (CLT) concept. The CLT states that for a non - normal population, as the sample size increases (usually \(n\geq30\) is a rule of thumb, but also, a larger sample relative to the population (when the population is finite) can still be used for inference as long as the sampling is random).

First, calculate the sample sizes:

• For Jason: The population size \(N = 25000\). The percentage of the population in his sample is \(0.24\%=0.0024\). So the sample size \(n_J=25000\times0.0024 = 60\).
• For Yolanda: The percentage of the population in her sample is \(0.27\% = 0.0027\). So the sample size \(n_Y=25000\times0.0027=67.5\approx68\) (we can consider the sample size as a whole number, and even if we take 67, it is still a reasonably large sample).

Since both sample sizes are greater than 30 (a common threshold for the CLT to apply approximately, even for non - normal populations) and the sampling is simple random sampling, both samples can be used to make inferences about the population.

Answer:

both Jason's sample and Yolanda's sample