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?(1.)To estimate the percentage well, she would need to collect data for all 35,000 families. (2.) 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. (3.) 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. (4.) 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.

Answer 1

I think the answer is 4.

Answer 2

Let's go through each of these answers.

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

The key word here is estimate. If she collected the data for all 35,000 families, that would not be estimating. 

This is false.

(2.) 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.

You don't need a certain number of samples to have a good estimate for the percentage of all 35,000 families that own a computer. 

This is false.

(3.) 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.

Since 45% of the 500 families she randomly selected had a computer, she can estimate that 45% of the 35,000 families in her town have a computer.

This is true.

(4.) 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.

The more samples you have the better your estimate will be.

This is true.

Hope this helps! :)