A polling company conducts an annual poll of adults about political opinions. Th
ID: 3157568 • Letter: A
Question
A polling company conducts an annual poll of adults about political opinions. The survey asked a random sample of 414 adults whether they think things in the country are going in the right direction or in the wrong direction. 53?% said that things were going in the wrong direction. Complete parts a and b below.
itions required to apply a confidence interval met? the sample proporto is between A. Yes, because the sample is a simple random sample, the sample proportion is between 10% and 90%, and there are at least 20 expected "successes" and 20 expected "failures." Yes, because the sample is a simple random sample, the sample is less than 10% of the population, and there are at least 10 expected "successes" and 10 expected "failures." B. ° C. No, because the sample is a simple random sample, the sample is less than 10% of the population, and there are at least 10 expected "successes" and 10 expected "failures." No, because the sample is a simple random sample, the sample proportion is between 10% and 90%, and there are at least 20 expected successes" and 20 expected "failures." D. b) How many people would need to be surveyed for a 90% confidence interval to ensure the margin of error would be less than 5%? n= (Round up to the nearest integer)Explanation / Answer
a)
OPTION B. [ANSWER]
[Note: It is usually option B, because we need a sample that is a small part of the population, but big enough to produce at least 10 successes and failures. However, if in some case you use option A in your class, please feel free to do so. Thanks!]
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b)
Note that
n = z(alpha/2)^2 p (1 - p) / E^2
where
alpha/2 = 0.05
Using a table/technology,
z(alpha/2) = 1.644853627
Also,
E = 0.05
p = 0.53
Thus,
n = 269.5803498
Rounding up,
n = 270 [ANSWER]