Question

Surveys tend to suffer from low response rates. Based on past​ experience, a researcher determines that the typical response rate for an​ e-mail survey is 30​%. She wishes to obtain a sample of 300 ​respondents, so she​ e-mails the survey to 2000 randomly selected​ e-mail addresses. Assuming the response rate for her survey is 30​%, will the respondents form an unbiased​ sample? Explain. Is the sample​ unbiased?

A. Yes. The sample was a randomly selected group of​ e-mail addresses, which does not introduce bias.
B. No. The survey still suffers from undercoverage​ (sampling bias), nonresponse​ bias, and potentially response bias.
C. No. The survey was not given to the entire population.
D. Yes. The number of respondents will be approximately 600​, that​ is, two times greater than the needed size of the sample.

Answer 1

B.

Explanation:

First let's define the different bias that exist:

Sampling bias: This bias occurs when the method used to get the sample favours one part of the population leaving another part of the population excluded.

Non response bias: This bias occurs when the people who do not answer the survey have different opinions from the ones who do.

Response bias: This bias occurs when the answer given to the survey does not reflect the true feelings of the person who responds.

Now back to the problem:

• The researcher sent the survey to 2000 randomly selected e-mail addresses, she expects to get 20% of responses, meaning 400 people will answer the survey.

Given these conditions, we would expect the survey to be biased. We have approximately 1600 people who didn't answer the survey so it is possible that all these people who didn't answer have different opinions from the 400 who did (non response bias), given that the survey was done by email it could also happen that people do not tell the truth when asked about a topic (response bias), also, there would be sampling bias because the people who she selected have an email address so the people who don't use email get excluded from the survey (sampling bias)