A bond proposal for school construction will be submitted to the voter

Question

A bond proposal for school construction will be submitted to the voters at the next municipal election. A major portion of the money derived form this bond issue will be used to build schools in a rapidly developing selection of the city, and the remainder will be used to renovate and update school buildings in the rest of the city. To assess the viability of the bond proposal, a random sample of-50 residents in the developing section and n100 residents from the other parts of the city were asked whether they plan to vote for the proposal. The results are tabulated below

Sample Values for Opinion on Bond Proposal

	Developing Section	Rest of the City
Sample size	50	100
Number favoring proposa	38	65

(a) Estimate the difference in the true proportions favoring the bond proposal with a 99% confidence interval.

(b) If both samples were pooled into one sample of size n-150, with 103 in favor of the proposal, provide a point estimate of the proportion of city residents who will vote for the bond proposal.

20 Feb 2025

Answer :

Word Count : 285

(a) To estimate the difference in the true proportions favoring the bond proposal with a 99% confidence interval, we use the formula for the confidence interval of the difference in proportions:

\[
CI = (\hat{p}_1 - \hat{p}_2) \pm Z_{\alpha/2} \sqrt{\frac{\hat{p}_1(1-\hat{p}_1)}{n_1} + \frac{\hat{p}_2(1-\hat{p}_2)}{n_2}}
\]

Where:
- \(\hat{p}_1 = \frac{\text{Number favoring proposal in developing section}}{n_1} = \frac{38}{50} = 0.76\)
- \(\hat{p}_2 = \frac{\text{Number favoring proposal in rest of the _________ ____ ________ _______ _____.
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Campaign
1	2	3
0.33	0.28	0.21
0.29	0.41	0.30
0.21	0.34	0.26
0.32	0.39	0.33
0.25	0.27	0.31

	Region
	1	2
Sample size	100	100
Sample mean	2.4	3.1
Sample variance	1.44	2.64

Student	With Imagery	Without Imagery	Student	With Imagery	Without Imagery
1	20	5	11	17	8
2	24	9	12	20	16
3	20	5	13	20	10
4	18	9	14	16	12
5	22	6	15	24	7
6	19	11	16	22	9
7	20	8	17	25	21
8	19	11	18	21	14
9	17	7	19	19	12
10	21	9	20	23	12