3. It seems to you that less than half of people who are registered voters in th
ID: 3358139 • Letter: 3
Question
3. It seems to you that less than half of people who are registered voters in the City of Madison do in fact vote in an election that is not for the president. You would like to know if this is true. In a simple random sample of 220 registered voters in the City of Madison, it is seen that 122 of them voted in the last non-presidential election (a) How might a simple random sample have been gathered? (b) Construct a 95% confidence interval to estimate the true proportion of voter turnout in the City of Madison. (c)Interpret your interval. (d) What conclusion can you draw about the whether or not less than half the people who are registered in the City of Madison voted?Explanation / Answer
a.
simple random possible,
possibile chances (x)=122
sample size(n)=220
success rate ( p )= x/n = 0.5545
b.
TRADITIONAL METHOD
given that,
possibile chances (x)=122
sample size(n)=220
success rate ( p )= x/n = 0.5545
I.
sample proportion = 0.5545
standard error = Sqrt ( (0.5545*0.4455) /220) )
= 0.0335
II.
margin of error = Z a/2 * (stanadard error)
where,
Za/2 = Z-table value
level of significance, = 0.05
from standard normal table,left tailed z /2 =1.645
margin of error = 1.645 * 0.0335
= 0.0551
III.
CI = [ p ± margin of error ]
confidence interval = [0.5545 ± 0.0551]
= [ 0.4994 , 0.6097]
-----------------------------------------------------------------------------------------------
DIRECT METHOD
given that,
possibile chances (x)=122
sample size(n)=220
success rate ( p )= x/n = 0.5545
CI = confidence interval
confidence interval = [ 0.5545 ± 1.645 * Sqrt ( (0.5545*0.4455) /220) ) ]
= [0.5545 - 1.645 * Sqrt ( (0.5545*0.4455) /220) , 0.5545 + 1.645 * Sqrt ( (0.5545*0.4455) /220) ]
= [0.4994 , 0.6097]
-----------------------------------------------------------------------------------------------
c.
interpretations:
1. We are 95% sure that the interval [ 0.4994 , 0.6097] contains the true population proportion
2. If a large number of samples are collected, and a confidence interval is created
for each sample, 95% of these intervals will contains the true population proportion
d.
we conclude that less than half of the people who registered voters in the city of madison do fact in election
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.