Question

(1 point) a senator wants to know what the voters of his state think of proposed legislation on gun control. he mails a questionnaire on the subject to an srs of 2500 voters in his state. his staff reports that 448 questionnaires have been returned, 343 of which support the legislation.
(a) this is an example of
a. a survey with little bias because it was the voters who elected the senator.
b. a survey with little bias because a large srs was used.
c. a survey containing nonresponse.
d. all of the above.
(b) the sample is
a. the 448 letters received.
b. the 2500 voters receiving the questionnaire
c. the 343 letters supporting the legislation.
d. the voters in his state.
(c) the population is
a. the voters in his state.
b. the 448 letters received.
c. the 2500 voters receiving the questionnaire.
d. the 343 letters supporting the legislation.
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Explanation:

Part (a)

• Option A: Just because voters elected the senator doesn't mean the survey has little bias. Non - response can still introduce bias.
• Option B: A large SRS was sent, but many (2500 - 448 = 2052) didn't respond. Non - response bias is present, so it's not a survey with little bias.
• Option C: Out of 2500 questionnaires mailed, only 448 were returned. This is non - response (some voters didn't respond to the survey), so this option is correct.
• Option D: Since A and B are incorrect, D is incorrect.

• The sample is the group from which we get data. The senator mailed questionnaires to 2500 voters (an SRS), and we consider the 2500 voters who received the questionnaire as the sample (even though not all responded, the sample is the group selected for the survey).
• Option A: The 448 letters received are the responses, not the sample.
• Option B: The 2500 voters receiving the questionnaire are the sample (the group we are trying to get data from).
• Option C: The 343 letters supporting are part of the responses, not the sample.
• Option D: The voters in his state are the population, not the sample.

• The population is the entire group we are interested in studying. The senator wants to know what the voters of his state think, so the population is all the voters in his state.
• Option A: The voters in his state are the population (the entire group of interest).
• Option B: The 448 letters received are responses, not the population.
• Option C: The 2500 voters receiving the questionnaire are the sample, not the population.
• Option D: The 343 letters supporting are part of the responses, not the population.

Answer:

C. a survey containing nonresponse.

Part (b)