, Problem 6 In early polls, respondents are often asked if they would vote for a

Question

, Problem 6 In early polls, respondents are often asked if they would vote for a generic Democrat or a generic Republican due to lack of knowledge of who the candidates will be. In a poll for the 2018 midterm elections, a pollster conducts a survey asking registered voters if they were more likely to vote for a generic Democrat or a generic Republican. Use the data in Excel to answer the following questions. a. Calculate a 95% confidence interval for the proportion of registered voters who plan on voting for the generic Democrat. (You may use Excel, but be sure you can calculate the interval by hand.) b. Using the interval from part (a), can you conclude that the proportion of people who plan on voting for a generic Democrat a minority? Why or why not? C. After seeing the initial results, the pollster feels that voters in Central Pennsylvania were overrepresented. They survey 50 additional people from metropolitan areas, 40 of whom say they would vote for a generic Democrat Calculate the new 95% confidence interval. d. Despite adding 50 people to the sample, the width of the interval in part (c) is the same as the width of the interval in part (a). Why is this the case?

Explanation / Answer

PART A.
TRADITIONAL METHOD
given that,
possibile chances (x)=555
sample size(n)=1187
success rate ( p )= x/n = 0.4676
I.
sample proportion = 0.4676
standard error = Sqrt ( (0.4676*0.5324) /1187) )
= 0.0145
II.
margin of error = Z a/2 * (stanadard error)
where,
Za/2 = Z-table value
level of significance, = 0.05
from standard normal table, two tailed z /2 =1.96
margin of error = 1.96 * 0.0145
= 0.0284
III.
CI = [ p ± margin of error ]
confidence interval = [0.4676 ± 0.0284]
= [ 0.4392 , 0.496]
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DIRECT METHOD
given that,
possibile chances (x)=555
sample size(n)=1187
success rate ( p )= x/n = 0.4676
CI = confidence interval
confidence interval = [ 0.4676 ± 1.96 * Sqrt ( (0.4676*0.5324) /1187) ) ]
= [0.4676 - 1.96 * Sqrt ( (0.4676*0.5324) /1187) , 0.4676 + 1.96 * Sqrt ( (0.4676*0.5324) /1187) ]
= [0.4392 , 0.496]
-----------------------------------------------------------------------------------------------
interpretations:
1. We are 95% sure that the interval [ 0.4392 , 0.496] 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

PART B.
we don't have evidence to support as the interval achived is less than 0.50 , [0.4392 , 0.496]

PART C.
given that,
possibile chances (x)= 555 + 40 = 595
sample size(n)= 1187 + 50 = 1237
success rate ( p )= x/n = 0.481
CI = confidence interval
confidence interval = [ 0.481 ± 1.96 * Sqrt ( (0.481*0.519) /1237) ) ]
= [0.481 - 1.96 * Sqrt ( (0.481*0.519) /1237) , 0.481 + 1.96 * Sqrt ( (0.481*0.519) /1237) ]
= [0.4532 , 0.5088]

PART D.
the width will vary as the reason proportion rate is increased with adding 50 of size who among 4 are democrates

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