Researchers will conduct a study of the television-viewing habits of children. They will select a simple random sample of children and record the number of hours of television the children watch per week. The researchers will report the sample mean as a point estimate for the population mean. Which of the following statements is correct for the sample mean as a point estimator?

Summary Submit Skip Question

Generally, a smaller sample size results in more variablility. Having a large dataset will cause an estimate to trend towards the true value (law of large numbers).

This is also evident in the equation for standard deviation for population mean:

$$ \sigma_{\bar{X}} = \frac{\sigma}{\sqrt{n}} $$

As \(n\) gets larger, the value for standard deviation gets smaller. Hence variability decreases and the point estimator approaches the true value.

Bias has more to do with how the sample was obtained.