Question

A survey of 250 voters was conducted to determine who they would vote for in an upcoming election for sheriff. Fifty-five 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

Answer 1

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*(1-p)*(z/E)2=	1057.00