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 100students or an SRS of 50students? Explain your answer.

Short Answer

Expert verified

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

01

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.

02

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.

03

Part (b) Step 1: Given Information

We are given two random samples of students.

50students random samples

100students random samples

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

04

Part (b) Step 2: Explanation

An SRS of 100students 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.

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