Question 1121480: A researcher wishes to estimate, with 99% confidence, the population proportion of adults who are confident with their country's banking system. His estimate must be accurate within 3% of the population proportion.
(a) No preliminary estimate is available. Find the minimum sample size needed.
(b) Find the minimum sample size needed, using a prior study that found that 26% of the respondents said they are confident with their country's banking system.
(c) Compare the results from parts (a) and (b).
(a) What is the minimum sample size needed assuming that no prior information is available?
nequals
nothing (Round up to the nearest whole number as needed.)
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! Use a proportion of 0.5 for the most conservative (largest sample size)
half-interval is 0.03
z*SE=0.03, z=2.576, SE is sqrt (.25/n)
square both sides
6.64*0.25/n=0.0009
multiply by n, divide by 0.0009
n=1.66/0.0009, or 1844.44 or 1845
The half-interval has width of 0.03
that equals z 0.995*sqrt [(0.26*0.74)/n], and z is 2.576
square both sides
6.64*0.1924/n=0.0009
multiply through by n, divide by 0.0009
1.278=0.0009n
n=1420 people
The further the proportion is from 0.5, the smaller the sample size needed. As an aside, if one is willing to lower the confidence interval to 90% or even less and increase the margin of error, which is not unreasonable for many satisfaction surveys, the sample size can be surprisingly small, although one needs to randomly select AND make sure all respond. A way around that is to assume non-respondents reply in a way that is not desired. That is a very conservative survey.
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