SOLUTION: A researcher wishes to​ estimate, with 99​% ​confidence, the population proportion of adults who say chocolate is their favorite ice cream flavor. Her estimate mu
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Question 1044003: A researcher wishes to estimate, with 99% confidence, the population proportion of adults who say chocolate is their favorite ice cream flavor. Her estimate must be accurate within 4% of the population proportion.
(a) No preliminary estimate is available. What is the minimum sample size needed.
(b) Find the minimum sample size needed, using a prior study that found that 38% of the respondents said their favorite flavor of ice cream is chocolate.
(c) Compare the results from parts (a) and (b).
(a) What is the minimum sample size needed assuming that no prior information is available? (Round up to the nearest whole number as needed.)
(b) What is the minimum sample size needed using a prior study that found that 38% of the respondents said their favorite ice cream flavor is chocolate? Round up to the nearest whole number as needed.)
(c) How do the results from (a) and (b) compare?
A.Having an estimate of the population proportion has no effect on the minimum sample size needed.
B.Having an estimate of the population proportion reduces the minimum sample size needed.
C.Having an estimate of the population proportion raises the minimum sample size needed.
Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
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(a)
:
since p is unknown, we use p = 0.5 and (p(1-p)) = 0.25
n = (Z(alpha/2))^2 * (0.25) / (0.04)^2
Z(alpha/2) = 2.575 from z-tables
n = (2.575)^2 * (0.25) / (0.04)^2 = 1036.0352
minimum sample size is 1036
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(b)
p = 0.38 and (0.38(1-0.38)) = 0.2356
n = (2.575)^2 *(0.2356) / (0.04)^2 = 976.3595
minimum sample size is 976
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:
answer is B) - having an estimate of the population proportion reduces the minimum sample size
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