Question

to estimate the mean number of text messages sent by cell phone users, a researcher chooses a location on a college campus in the city and surveys the first 50 people who walk past. these subjects are asked how many text messages they have sent in the past 24 hours. is it likely that bias will be present in the sample?

• because this is a convenience sample, it is likely that the sample results will be unbiased.
• because this is a convenience sample of college students, it is likely that bias is present and that the results will overestimate the mean number of text messages sent.
• because this is a convenience sample of college students, it is likely that bias is present and that the results will underestimate the mean number of text messages sent.
• because this is a voluntary response sample of college students, it is likely that bias is present and that the results will overestimate the mean number of text messages sent.

Explanation:

This is a question about sampling bias in statistics (a subfield of Mathematics). The researcher used a convenience sample (surveying the first 50 people on a college campus), which only includes college students. College students may send more text messages than the general population of cell - phone users. So this sample is not representative of all cell - phone users, and the results are likely to overestimate the mean number of text messages sent by all cell - phone users. Now let's analyze each option:

• Option 1: A convenience sample is likely to be biased, not unbiased, so this is wrong.
• Option 2: Since college students are more likely to send more texts than the general population, the sample (college students) will overestimate the mean for all cell - phone users. This option is correct.
• Option 3: As explained, the sample is likely to overestimate, not underestimate, so this is wrong.
• Option 4: This is a convenience sample, not a voluntary response sample (voluntary response samples are when people choose to respond, like in a call - in survey), so this is wrong.

Answer:

B. Because this is a convenience sample of college students, it is likely that bias is present and that the results will overestimate the mean number of text messages sent.