any statistics pros out there?

Question

I really really want to get this right...

A poll shows that one presidentail candidate  has a 51% of the vote, and the other has  47% of the vote. The poll was given by phone to s random sample  of 1157 voters. The stated margin of error  is 3% at the 95% confidence level.

Which of the following statements describes the meaning of the margin of error?

a. The first candidate will win the election because that candidate  is ahead  by more than three  percentage points. 

b. The first candidate has a 95% chance of winning the election.

c. The second candidate has between a 44% chance and 50% chance of winning.

d. There is a 95% chance the second candidate will receieve between 44%  and 50% of the vote.

Help!!  I am thinking it must be d, but I have no idea why.

Thanks!!

Jay G · Accepted Answer

D is correct.  3% margin of error is just that.  The estimate given may be up to 3% too high or too low.  95% confidence level means that 95% of the time the condition will be met.  In this case the condition is the margin of error is + or - 3%.

a is not correct.  The polls are prone to error and cannot predict with certainty the winner

b is not correct.  95% confidence level refers to the probability of the error being within -3% to +3%, not the chace of winning

c is not correct.  Again they are applying the wrong pieces together.  The % of the vote is subject to margin, not the % chance of winning.

d is corrrect per opening comment

Anonymous · Answer

Answer is d, as the 95% confidence intervals, give 95 % chance that the population proportion is within 3 % either side of the sample proportion of 47%, which is the interval between 44% and 50%.

Hope this helps, if so it may just be the BEST ANSWER he he, just kidding but no really it is the best answer,.

The Lord Of Combinatorics · Answer

Yes you are correct. That is the definition of confidence level.

a confidence level of lets say 95% with a margin of error y% means that there is a 95% chance that the final outcome will be between your predicted outcome + or - y

any statistics pros out there?

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