Question

g. if you were to use a random sample of size 20 to estimate the population mean, would you expect the estimate to be closer to or farther from the actual value of the population mean than if you had used a random sample of size 10? would this mean that the margin of error would be less than or greater than the margin of error for a sample of size 10?

Explanation:

Step1: Recall Sample Size & Estimation

Larger sample size (n) reduces sampling variability. A sample of size 20 has less variability than n=10, so the estimate (sample mean) is closer to population mean.

Step2: Recall Margin of Error (ME) Formula

For estimating population mean, \( ME = z^*\frac{\sigma}{\sqrt{n}} \) (or \( t^*\frac{s}{\sqrt{n}} \)). As \( n \) increases, \( \sqrt{n} \) increases, so \( ME \) decreases. Thus, ME for n=20 is less than for n=10.

Answer:

For a sample of size 20, the estimate is closer to the population mean. The margin of error for a sample of size 20 is less than the margin of error for a sample of size 10.