Question

Catherine finds that in a randomly selected sample of 500 families in her home town, 45% own at least one computer. Her research shows that there are a total of 35,000 families in her town.

Which statements are true? Select EACH correct answer.



A If she collected data for a random sample of 1000 families in her home town, then that percentage would be a better estimate for the percentage of all 35,000 families that own a computer.


B Since her sample was randomly selected, she can reasonably infer that about 45% of the 35,000 families in her town own at least one computer.


C To estimate the percentage well, she would need to collect data for all 35,000 families.


D Since her sample was only 500 families, it is not possible that the percentage is a good estimate for the percentage of all 35,000 families that own a computer.

Answer 1

Catherine selected a random sample of 500 families, out of a possible 35,000 families. Because the population is large, her sample size should have also been a little bit larger than 500. In this case, the correct answers are A and D, because selecting more families to sample would have represented the population better.