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27 December, 18:29

A city ballot includes a local initiative that would legalize gambling. The issue is hotly contested, and two groups decide to conduct polls to predict the outcome. The local newspaper finds that 47 % of 2300 randomly selected voters plan to vote "yes," while a college Statistics class finds 46 % of 500 randomly selected voters in support. Both groups will create 99 % confidence intervals. Assume that all voters know how they intend to vote and that the initiative requires a major?

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  1. 27 December, 20:35
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    A) 2.02 standard deviations from 600 - a win

    B) The last interval was a close call.

    Explanation:

    n = 2300

    p = 0.47, q = 1-p = 0.53

    μ = np = 1081

    σ = √ (npq) = 23.94

    Z. 025 = 1.96

    B) Finding both confidence interval:

    Confidence Interval = (μ-1.96 (23.94) / √2300, μ+1.96 (23.94) / √2300)

    = (1081 - 0.978, 1081 + 0.978)

    = (1080.022, 1081.978)

    (1080-600) / 23.94 = 2.02 standard deviations from 600 - a win

    B)

    AS above

    n=450, p=.54, q=.46

    μ=np=243, σ=√ (npq) = 10.6

    confidence interval (243-1.96 (10.6) / √450, 243+1.96 (10.6) / √450)

    = 243-.98, 243+.98) = (242.0, 243.98)

    (244-225) / 10.6=1.8 standard deviations from win
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