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A researcher would like to estimate p, the proportion of U.S. adults who support recognizing civil unions between gay or lesbian couples.
Question
A researcher would like to estimate p, the proportion of U.S. adults who support recognizing civil unions between gay or lesbian couples.
If the researcher would like to be 95% sure that the obtained sample proportion would be within 1.5% of p (the proportion in the entire population of U.S. adults), what sample size should be used?
(a) 17,778
(b) 4,445
(c) 1,112
(d) 67
(e) 45
Due to a limited budget, the researcher obtained opinions from a random sample of only 2,222 U.S. adults. With this sample size, the researcher can be 95% confident that the obtained sample proportion will differ from the true proportion (p) by no more than (answers are rounded):
(a) .04%
(b) .75%
(c) 2.1%
(d) 3%
(e) There is no way to figure this out without knowing the actual sample proportion that was obtained.
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Mathematics
3 years
2021-08-06T21:57:33+00:00
2021-08-06T21:57:33+00:00 1 Answers
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Answers ( )
Answer:
Question 1:
(b) 4,445
Question 2:
(c) 2.1%
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of
, and a confidence level of
, we have the following confidence interval of proportions.
In which
z is the zscore that has a pvalue of
.
The margin of error is of:
95% confidence level
So
, z is the value of Z that has a pvalue of
, so
.
Question 1:
We have no previous estimate for the population proportion, so we use
.
The sample size is n for which M = 0.015. So
Samples above this value should be used, and the smaller sample above this value is of 4445, so the answer is given by option b.
Question 2:
Now we find M for which
.
So 2.1%, and the correct answer is given by option c.