Suppose a bond proposal for school construction will be submitted to voters at t

Question

Suppose a bond proposal for school construction will be submitted to voters at the next municipal election. A major portion of the money will be used to build schools in a rapidly “developing” section of the city whereas the remaining money will be used to update current school buildings. To assess the viability of the proposal, a random sample of 50 residents who live in the developing section of the city was selected and an independent random sample of 100 residents who do not live in the developing section of the city was selected. All 150 residents were asked how they plan to vote for the proposal. The results are summarized below.

Question 5 Background: Comparing Rates for Favoring Bond Proposal Suppose a bond proposal for school construction will be submitted to voters at the next municipal election. A major portion of the money will be used to build schools in a rapidly "developing" section of the city whereas the remaining money will be used to update current school buildings. To assess the viability of the proposal, a random sample of 50 residents who live in the developing section of the city was selected and an independent random sample of 100 residents who do not live in the developing section of the city was selected. All 150 residents were asked how they plan to vote for the proposal. The results are summarized below 1- Developing Section 50 38 0.76 Outside Developing Section Sample size # Favoring Proposal Proportion in Favor 100 65 0.65 Let p1 represent the population proportion of all residents of the developing section that are in favor of the proposal, and p2 represent the population proportion of all residents from outside the developing section that are in favor of the proposal Question 5 Subquestions Estimate the difference in the two population proportions p1-P2 1 point(s) No answer entered. Click above to enter an answer 5.b Provide the 99% confidence interval estimate for the difference in the population rate of favoring the proposal for all residents of the developing section as compared to all residents from outside the developing section 2 point(s) No answer entered. Click above to enter an answer 5.C A 90% confidence interval based on the same data would result in an interval that is the 99% confidence interval point(s) wider than narrower than the same width as

Explanation / Answer

a)

Getting p1^ and p2^,          
          
p1^ = x1/n1 =    0.76      
p2 = x2/n2 =    0.65      

hence,

p1^ - p2^ = 0.11 [ANSWER]

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b)
          
Also, the standard error of the difference is          
          
sd = sqrt[ p1 (1 - p1) / n1 + p2 (1 - p2) / n2] =    0.076961029      
          
For the   99%   confidence level, then  
          
alpha/2 = (1 - confidence level)/2 =    0.005      
z(alpha/2) =    2.575829304      
Margin of error = z(alpha/2)*sd =    0.198238474      
lower bound = p1^ - p2^ - z(alpha/2) * sd =    -0.088238474      
upper bound = p1^ - p2^ + z(alpha/2) * sd =    0.308238474      
          
Thus, the confidence interval is          
          
(   -0.088238474   ,   0.308238474 ) [ANSWER]

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c)

Lower confidence levels yield narrower confidence intervals. Hence,

OPTION B: NARROWER THAN. [ANSWER]

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d)

We need the sample sizes to be at least 30.

OPTION B: The sample sizes 50 and 100 ar eboth at least 30. [ANSWER]

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