wishes to estimate, with 90% confidence the population roportion of adults who a
ID: 2931094 • Letter: W
Question
wishes to estimate, with 90% confidence the population roportion of adults who are confident with ther countr s banking s ste n His estimate must be accurate within 5% of the population (a) No preliminary estimate is available. Find the minimum sample size needed b Find the minimum sample size needed, using a prior stud ' that found that 32% of the respondents sad they are confident with their countr (c) Compare the results from parts (a) and (b) s banking system. (Round up to the nearest whole number as needed,) (b What s e minimum sam e s ze needed sr a p or study that found that 32% of the respondents sad they are confident with their co ne(Round up to the nearest whole number as needed ) (c) How do the results from (a) and (bl compare? s banking system?Explanation / Answer
(a)
If no prior estimate is available, we can assume p = 0.5
Margin of error = 0.05
z-value for 90% CI = 1.65
ME = z * SE
ME = z * sqrt(p*(1-p)/n)
0.05 = 1.65 * sqrt(0.5 * 0.5/n)
n = (1.65/0.05)^2 / 0.25
n = 4356
(b)
p = 0.32
ME = z * SE
ME = z * sqrt(p*(1-p)/n)
0.05 = 1.65 * sqrt(0.32 * 0.68/n)
n = (1.65/0.05)^2 / (0.32 * 0.68)
n = 5004.60 i.e. 5005
(c)
Having an estimate of the population proportion raises the minimum sample size needed.
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