A survey of 250 voters was conducted to determine who they would vote for in an upcoming election for sheriff. Fiftyfive percent said they would vote for Longmire.
A/ What is the best unbiased estimate of the population
proportion that will vote for Longmire (in other words, what is
?)
B/ Find the margin of error E that corresponds to a 90% confidence
Interval.
C/ Construct the 90% confidence interval about the population
proportion p.
D/ Based on your results, can you conclude that Longmire will win
the sheriff
election?

E/ What sample size would be required to estimate the true
proportion of voters voting for Longmire within 3% at a 95%
confidence level? Assume P=0.55
a)
best unbiased estimate of the population proportion that will vote for Longmire =0.55
b)
from abvoe margin of errror =0.0518
c)90% confidence interval about the population proportion p =0.498 ;0.602
d)
as our confidence interval contains values below 0.50 proportion also; therefore we can not conclude that Longmire will win the sheriff election
e)
here margin of error E =  0.03  
for95% CI crtiical Z =  1.960  
estimated proportion=p=  0.550  
required sample size n =  p*(1p)*(z/E)^{2}=  1057.00 
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