Question 976486: 22. You Explain It! Superstition: A USA Today/Gallup poll asked 1,006 adult Americans how much it would bother them to stay in a room on the 13th floor of a hotel. Interestingly, 13% said it would bother them. The margin of error was 3 percentage points with 95% confidence. Which of the following represents a reasonable interpretation of the survey results? For those not reasonable, explain the flaw.
(a) We are 95% confident that the proportion of adult Americans who would be bothered to stay in a room on the 13th floor is between 0.10 and 0.16.
(b) We are between 92% and 98% confident that 13% of adult Americans would be bothered to stay in a room on the 13th floor.
Answer:
(c) In 95% of samples of adult Americans, the proportion who would be bothered to stay in a room on the 13th floor is between 0.10 and 0.16.
Answer:
(d) We are 95% confident that 13% of adult Americans would be bothered to stay in a room on the 13th floor.
Answer:
Found 2 solutions by Boreal, FrankM:
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! It is A.
B is wrong because that is confidence of a confidence. We don't have that.
D is wrong because it is an interval, not a point estimate.
C is the closest to being right, but use of proportion has to be very carefully done. I prefer to say that we don't know the exact proportion, but if we had 100 samples, 95% would contain the true proportion, whatever it is. We wouldn't know which samples they were. The problem with C is that it discusses the proportion in terms of an interval. It has to discuss it in terms of a specific number or parameter.
Answer by FrankM(1040)  (Show Source):
You can put this solution on YOUR website! (a) We are 95% confident that the proportion of adult Americans who would be bothered to stay in a room on the 13th floor is between 0.10 and 0.16.
Yes, this is the answer
(b) We are between 92% and 98% confident that 13% of adult Americans would be bothered to stay in a room on the 13th floor.
No, the 3% range applies to the data, not the confidence level.
(c) In 95% of samples of adult Americans, the proportion who would be bothered to stay in a room on the 13th floor is between 0.10 and 0.16.
No, repeated sampling doesn't apply.
(d) We are 95% confident that 13% of adult Americans would be bothered to stay in a room on the 13th floor.
No, where does the +/- 3% come in?
The wikipedia article on confidence level does a good job explaining this. https://en.wikipedia.org/wiki/Confidence_interval
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