SOLUTION: Please help..I have taking stats online and trying to teach myself...I am very confused on this problem....Thank you A sample of 147 golfers showed that their average score on

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Question 490312: Please help..I have taking stats online and trying to teach myself...I am very confused on this problem....Thank you
A sample of 147 golfers showed that their average score on a particular golf course was 91.85 with a standard deviation of 3.29.
Answer each of the following (show all work
and state the final answer to at least two decimal places.):

(A) Find the 90% confidence interval of the mean score for all 147 golfers.
(B) Find the 90% confidence interval of the mean score for all golfers if this is a sample of 125 golfers instead of a sample of 147.
(C) Which confidence interval is larger and why?
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
A sample of 147 golfers showed that their average score on a particular golf course was 91.85 with a standard deviation of 3.29.
Answer each of the following (show all work
and state the final answer to at least two decimal places.):
(A) Find the 90% confidence interval of the mean score for all 147 golfers.
xbar = 91.85
ME = 1.645*(3.29/sqrt(147) = 0.4464
--------
90% CI: 91.85-0.4464 < u < 91.85+0.4464
(91.4036,92.2964)
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(B) Find the 90% confidence interval of the mean score for all golfers if this is a sample of 125 golfers instead of a sample of 147.
xbar = 91.85
ME = 1.645 = 0.4841
(91.3659,92.3341)
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(C) Which confidence interval is larger and why?
The sample of 125 has a wider CI because 125 gives us
less information than a sample of 147.
The 125 sample has a larger margin of error(ME)
because the ME is always twice as wide as ME.
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Cheers,
Stan H.