It seems to you that fewer than half of people who are registered voters in the
ID: 3062388 • Letter: I
Question
It seems to you that fewer than half of people who are registered voters in the City of Madison do in fact vote when there is an election that is not for the president. You would like to know if this is true. You take an SRS of 200 registered voters in the City of Madison, and discover that 122 of them voted in the last non-presidential election.
(a) How might a simple random sample have been gathered?
(b) Construct a 90% CI to estimate the true proportion of registered voters in the City of Madison who vote in non-presidential elections.
(c) Interpret the interval you created in part (b).
(d) Based on your CI, does it seem that fewer than half of registered voters in the City of Madison vote in non-presidential elections? Explain.
Explanation / Answer
TRADITIONAL METHOD
given that,
possibile chances (x)=122
sample size(n)=200
success rate ( p )= x/n = 0.61
I.
sample proportion = 0.61
standard error = Sqrt ( (0.61*0.39) /200) )
= 0.0345
II.
margin of error = Z a/2 * (stanadard error)
where,
Za/2 = Z-table value
level of significance, = 0.1
from standard normal table, two tailed z /2 =1.645
margin of error = 1.645 * 0.0345
= 0.0567
III.
CI = [ p ± margin of error ]
confidence interval = [0.61 ± 0.0567]
= [ 0.5533 , 0.6667]
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DIRECT METHOD
given that,
possibile chances (x)=122
sample size(n)=200
success rate ( p )= x/n = 0.61
CI = confidence interval
confidence interval = [ 0.61 ± 1.645 * Sqrt ( (0.61*0.39) /200) ) ]
= [0.61 - 1.645 * Sqrt ( (0.61*0.39) /200) , 0.61 + 1.645 * Sqrt ( (0.61*0.39) /200) ]
= [0.5533 , 0.6667]
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interpretations:
1. We are 90% sure that the interval [ 0.5533 , 0.6667] contains the true population proportion
2. If a large number of samples are collected, and a confidence interval is created
for each sample, 90% of these intervals will contains the true population proportion
a.
sample will be randmoly chosen from a list of registered voters with in a madison city
b.
[0.5533 , 0.6667]
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interpretations:
1. We are 90% sure that the interval [ 0.5533 , 0.6667] contains the true population proportion
2. If a large number of samples are collected, and a confidence interval is created
for each sample, 90% of these intervals will contains the true population proportion
c.
the true proportion of registered voters in the City of Madison who vote in non-presidential elections
is above fifty percent
d.
since the confidence value is [0.5533 , 0.6667] , and which is above 50% and this result in we dno't have evidence that fewer then half
of registered voters in the City of Madison vote in non-presidential elections
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