Question

Question 1: "College parents. An online survey of college parents was conducted during February and March 2007. Emails were sent to 41,000 parents who were listed in either the College Parents of America database or the Student Advantage database. Parents were invited to participate in the online survey. Out of those invited, 1727 completed the online survey. The survey protected the anonymity of those participating in the survey but did not allow more than one response from an individual IP address.

One of the survey results was that 33% of mothers communicate at least once a day with their child while at school.

What was the response rate for this survey? (The response rate is the percentage of the planned sample—that is, those invited to participate—who responded.)
Use the quick method (page 43) to estimate the margin of error for a random sample of size 1727.
Do you think that the margin of error is a good measure of the accuracy of the survey’s results? Explain your answer."

Answer 1

The response rate for this survey was 4.2%, which is calculated by dividing the number of people who responded (1727) by the total number of people invited (41,000).

Using the quick method to estimate the margin of error, we can calculate that the margin of error for a random sample of size 1727 is approximately ±3%.

Yes, I think that the margin of error is a good measure of the accuracy of the survey's results. The margin of error tells us how close our sample estimates are to the true population parameter – in this case, the proportion of mothers who communicate at least once a day with their child while at school. This allows us to have more confidence in the results of the survey, since it shows that the results have a high degree of accuracy.