Help The company MasonDixon Polling and Research Inc conduct

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The company Mason-Dixon Polling and Research, Inc. conducted an opinion poll just prior to an election. The poll surveyed 625 potential voters, asking them whether they thought Walter Mondale was the best choice to replace Paul Wellstone. Of the 625 people polled, 344 answered that Mondale was the best choice. Does this sample give evidence that more than half of all potential voters thought Mondale was the best choice? Justify your answer with the appropriate statistical procedure.

1,the null and alternative hypothesis; the p-value;

2,the decision to reject the null hypothesis or fail to reject; and

3,a final conclusion sentence about the question in the problem.

Solution

1,the null and alternative hypothesis; the p-value;

Null hypothesis: p=0.5

Alternative hypothesis: p>0.5

The test statistic is

Z=(phat-p)/sqrt(p*(1-p)/n)

=(344/625-0.5)/sqrt(0.5*0.5/625)

=2.52

It is a right-tailed test.

So the p-value= P(Z>2.52) =0.0059 (from standard normal table)

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2,the decision to reject the null hypothesis or fail to reject; and

Assume that the significant level a=0.05

Since the p-value is less than 0.05, we reject the null hypothesis.

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3,a final conclusion sentence about the question in the problem.

So we can conclude that more than half of all potential voters thought Mondale was the best choice