When getting voters to support a candidate in an election, is there a difference between a recorded phone call from the candidate or a flyer about the candidate sent through the mail? A sample of 500 voters is randomly divided into two groups of 250 each, with one group getting the phone call and one group getting the flyer. The voters are then contacted to see if they plan to vote for the candidate in question. We wish to see if there is evidence that the proportions of support are different between the two methods of campaigning.
(a) Define the relevant parameter(s) and state the null and alternative hypotheses.
(b) Possible sample results are shown in Table 4.2. Compute the two sample proportions: p̂_c, the proportion of voters getting the phone call who say they will vote for the candidate, and p̂_f, the proportion of voters getting the flyer who say they will vote for the candidate. Is there a difference in the sample proportions?

Table 4.2

(c) A different set of possible sample results are shown in Table 4.3. Compute the same two sample proportions for this table.

(d) Which of the two samples seems to offer stronger evidence of a difference in effectiveness between the two campaign methods? Explain your reasoning.

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Will Vote Will Not Vote for Candidate for Candidate Sample A Phone call Flyer 152 145 98 105 Will Vote for Candidate Will Not Vote for Candidate Sample B Phone call Flyer 188 62 130 120