Question

The chairman of the local Democratic Party believes that more than 75% of the freshmen who have just arrived on campus have registered to vote in the upcoming election. Since it would be difficult to question all of the freshmen to determine the actual percentage, a random sample of 64 students was interviewed. Of these, 43 indicated that they are registered to vote.

At the .05 level of significance, is the assumption that more than 75% are registered still valid? You must state the hypotheses, a decision rule and a full conclusion for this problem. Use the Decision Rule method. Use of the p-value will result in a loss of credit.

Answer 1

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Hypothesis:

Ho: not more than 75% registered

Ha: More than 75% registered

test statistic will be calculated as below:

p = .75

n = 64, x = 43

p^ = x/n = (43/64) = .672

The p^ is not beyond 75% and therefore we conclude the following:

Conclusion: Since p^ is less than .75 we will conclude that the belief of the chairman that more than 75% of the freshmen who have just arrived on campus have registered to vote in the upcoming elections is WRONG