Question 155312: A mayoral election race is tightly contested.
In a random sample of 1,100 likely voters, 572 said that they were planning to vote for the current mayor.
Based on this sample, what is your initial hunch?
Would you claim with 95% confidence that the mayor will win a majority of the votes? Explain.
(create the 95% confidence interval... then explain)
Found 2 solutions by stanbon, jojo14344:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! 572/1100 = 0.52
Assuming that the mean is 0.5, the standard deviation is sqrt(0.5*0.5/1100)
= 0.015076
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For a 95% confidence interval the upper critical value is 0.5 + 1.96*0.015076
= 0.29548... = .529549
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since the sample proportion (0.52) is less than the critical value, you
cannot reject a hypothesis that there is a 50% chance of either candidate winning. You cannot be 95% confident that your candidate will win.
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Cheers,
Stan H.
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Answer by jojo14344(1513) (Show Source):
You can put this solution on YOUR website! To win the election, we know you should be win over 50% of the total votes.
In this case,  , and you should be more these votes to win. Now, if 572 said they were planning to vote for the current mayor, my initial hunch the mayor will WIN and that is based on 100% confidence -----> OVER 50% OF THE VOTE!
.
In 95% confidence, will the mayor wins? -------------> NO. why?
If you're only 95% of the total 572 will vote for the mayor, then the total will be below the 50%: ------>  , the mayor will loose.
That answers the question.
thank you,
Jojo
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