Question

Far from home? A researcher wants to estimate the average distance that students at a large community college live from campus. To find out, she surveys a simple random sample of students from the registrar’s database.

a. Will the researcher’s sample result be exactly the same as the true population's mean? Explain your answer.

b. Which would be more likely to produce a sample result closer to the true population value: an SRS of $100$students or an SRS of $50$students? Explain your answer.

Short answer

a.No, the researcher’s sample result will not be the same as the true population's mean.

b. An SRS of 100 students would be more likely to produce a sample result close to the true population value.

Step-by-step solution

Part (a) Step 1:Given Information

There are some random samples of students drawn by a researcher from the registrar’s database.

We need to explain will researcher's sample result will be exactly same as true population's mean.

Part (a) Step 2: Explanation

No, the researcher’s sample result will not be exactly the same as the true population's mean because different random samples will give us different statistics, and it is unlikely that these statistics will match the parameter exactly.

Part (b) Step 1: Given Information

We are given two random samples of students.

$50$students random samples

$100$students random samples

We need to explain which sample will give result closer to true population value

Part (b) Step 2: Explanation

An SRS of $100$students would be more likely to produce a sample result close to the true population value because larger samples will reduce the variability and give accurate results.