What sample size should be obtained if he wants to be within 2 percentage points
ID: 3159080 • Letter: W
Question
What sample size should be obtained if he wants to be within 2 percentage points with 96% confidence if he uses an estimate of 48% obtained to a poll? sample size is (Round up to the nearest integer.) What sample size should be obtained if he wants to be within 2 percentage points with 96% o confidence if he does not use any prior estimates? The sample size is Why are the results from parts (a) and (b) so close The results are close because the margin of error 2% is less than 5%. The results are close because the confidence 96% is close to 100% The results are close because 0.48(1-0.48) = 0.2496 is very close to 0.25.Explanation / Answer
a)
Note that
n = z(alpha/2)^2 p (1 - p) / E^2
where
alpha/2 = 0.02
Using a table/technology,
z(alpha/2) = 2.053748911
Also,
E = 0.02
p = 0.48
Thus,
n = 2631.959983
Rounding up,
n = 2632 [ANSWER]
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b)
Note that
n = z(alpha/2)^2 p (1 - p) / E^2
where
alpha/2 = 0.02
As there is no previous estimate for p, we set p = 0.5.
Using a table/technology,
z(alpha/2) = 2.053748911
Also,
E = 0.02
p = 0.5
Thus,
n = 2636.177867
Rounding up,
n = 2637 [ANSWER]
***********************************
c)
The results are close because the estimates, 48% and 50%, are close, so
OPTION C: The results are close because 0.48*(1-0.48) is close to 0.25. [ANSWER, C]
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