Far from home A researcher wants to estimate the average dis

Far from home? A researcher wants to estimate the average distance that students at a large community col- lege 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 mean? Explain.
(b)   Which would be more likely to get the researcher’s sample result closer to the true population value: an SRS of 100 students or an SRS of 50 students? Explain.

28.

Solution

a)The sample mean is an unbiased estimator of population mean. Thus, the sample mean will be exactly same with that of population mean.

b)Large sample sizes will definitely give result closer to the true population value, thus, an SRS of 100 students is more likely to give closer results.